Day 27 - CRACK SSC MATHS by DEO, Nizamabad Sri P.Ashok garu

追加: 2026-05-28

[00:06:40]respond.

[00:06:44]>> Yes sir.

[00:07:05]Okay. Right.

[00:07:48]Yes. Yesterday what we discussed difference of two sets, right?

[00:07:52]>> Yes sir.

[00:07:52]>> Yes sir.

[00:07:54]>> What is that problem? A = >> A = 1 2 3.

[00:08:00]>> Right.

[00:08:02]>> B = 2 = 2 3 7.

[00:08:07]>> Right.

[00:08:10]35 67.

[00:08:12]>> Huh?

[00:08:13]>> 35 67.

[00:08:16]>> 35 67. Right.

[00:08:18]>> Yes, sir.

[00:08:19]>> Yes, sir.

[00:08:27]Right.

[00:08:36]>> Right. Then what is the first one?

[00:08:41]>> A minus of B union C.

[00:08:52]What is B union C?

[00:08:53]>> 2 3 5 7 2 3 5 6 7 >> 2 3 7 2 >> 2 3 2 3 5 6 7 >> 7 6 5 >> 1 2 3 7 5 >> 7 6 7 >> becomes what?

[00:09:15]>> 2 3 7 567 >> 567 23 56 7 Right.

[00:09:24]>> Yes. Yes, sir.

[00:09:26]Union sus C means A= >> 1 2 3 1 1 2 3 2 3 - 2 3 5 3 5 6 7 Right.

[00:09:57]>> Yes sir. Yes sir. A minus of B union C = 1 2 3 2 cancel.

[00:10:05]>> Yes sir.

[00:10:09]>> 1 second one.

[00:10:16]A minus B union of A minus C, >> right?

[00:10:29]>> What is >> 1 2 3?

[00:10:34]>> 1 2 3 - 2 3 7 2 3 7 A minus b = 1 1 >> right?

[00:10:51]>> Yes sir.

[00:10:52]>> Yeah. A minus C >> 1 2 3 4 >> 3 - 3 5 6 7 >> A - C = 1 and 2 >> 2 >> 1 2 right?

[00:11:13]>> Yes sir.

[00:11:13]>> Yes sir.

[00:11:14]>> What about their union?

[00:11:17]A minus B >> one union 1 2 1 2 >> these two are 1 and two are same >> no sir >> no sir >> here first set B union single set one here one these two are different right yes sir yes sir Third one we check.

[00:11:50]>> What is third one? A minus B intersection C.

[00:11:58]>> H. First we have to find B intersection C. Right.

[00:12:01]>> Yes.

[00:12:02]>> What is Ba 3 7 >> 4 3 7 >> intersection? What is >> 3a 5a 6a 7?

[00:12:13]Six.

[00:12:14]>> Very six.

[00:12:18]>> Yes.

[00:12:19]>> Yes.

[00:12:20]>> 3= to three and seven >> and common >> common terms.

[00:12:29]>> Yes. Common in both sets, right?

[00:12:31]>> Yes.

[00:12:33]>> Common elements. Common elements are 3a 7. B intersection. Next.

[00:12:38]A >> AU B intersection C >> B intersection C >> 1 2 3 >> 37 >> 3 gets cancelled of B intersection= 1 2 1 second and third and third are equal right equal. Yes sir. Yes sir. Next fourth a minus b intersection >> of a cus.

[00:13:19]>> What is a minus b?

[00:13:21]>> 1 2 3 - 2 37 >> 2 3 7 >> 2 3 2 3 gets cancelled only singleton one.

[00:13:34]>> Yeah sir. A - = 1 2 3 - 3 5 6 7 >> 1 >> 3 5 6 7 >> 7 >> 7 >> 3 R 2 1 comma 2 Action 192.

[00:14:03]>> What is the intersection?

[00:14:04]>> It is one.

[00:14:07]the first and fourth one is equal.

[00:14:11]>> Therefore, we conclude that A minus of B union C is equal to A minus B intersection >> A minus C.

[00:14:27]>> This union will become intersection, right?

[00:14:30]>> Yes sir.

[00:14:30]>> Yes sir.

[00:14:33]A minus or B intersection C is equal to A minus B union >> A minus C.

[00:14:42]>> Right? Got it?

[00:14:43]>> Yes sir.

[00:14:51]That is the difference of two sets, right?

[00:14:53]>> Yes sir. Yes sir.

[00:14:54]>> Yes sir.

[00:15:04]Yesterday we discussed about universal set right?

[00:15:07]>> Yes sir.

[00:15:07]>> Yes sir.

[00:15:09]>> Universal set means >> collects all elements relative to situation or context right?

[00:15:17]>> Yes sir. It is denoted with mu sir.

[00:15:20]>> Denoted with mu right?

[00:15:22]>> Yes sir.

[00:15:24]Next.

[00:15:39]>> What is the next one?

[00:15:41]>> Complement of a set.

[00:15:43]>> Complement of a set.

[00:15:51]API is any set its complement is denoted with a dash or a complement defined Yes.

[00:16:23]Set of elements in universal set and but not U but not in A.

[00:16:46]Yes. Tell then the definition of complement of a set.

[00:16:50]If any set is denoted with a complemented set of elements but not as set of elements >> universal >> but not in a >> elements present in universal set but not in A.

[00:17:11]>> Right?

[00:17:12]>> Yes sir.

[00:17:14]>> Therefore what is the A complement?

[00:17:18]A complement equal to yes present in mu but not in A.

[00:17:24]Yes sir.

[00:17:25]>> That is nothing but equal >> equal to present in mu but not in a how to represent it. Sorry. A dash is equals to 1 2 3 = 1 2 3 4 5 6 1 2 3 4 5 >> Oh yeah.

[00:17:50]>> Then a dash is equal to what? A= 1 2 3 m = 1 2 3 4 What is a dash?

[00:18:01]Yes.

[00:18:04]Following >> sir >> a = listen please a = 1 2 3 universal set mu= 1 2 3 4 then a dash equal to what >> present in universal set but not in a >> present in universal set but not in a only four.

[00:18:32]>> Yes sir. Right. Very good. Who told that?

[00:18:35]>> Four.

[00:18:36]>> That's dura.

[00:18:37]>> Okay. Good. Four only. Right.

[00:18:41]Four is present in universal set but not in a here. A dash. How to denote? What is the definition?

[00:18:46]Present invers but not in a equal.

[00:18:52]>> It is equal to what?

[00:18:57]>> General in general present in universal not in a. How to write that one in symbolic?

[00:19:06]Present in A but not in B means what?

[00:19:11]Present in A but not in B means a B.

[00:19:17]>> No no no. A B are any two sets? Elements present in A but not in B.

[00:19:24]A minus B.

[00:19:28]What is A minus B?

[00:19:31]difference in J but not in a >> A minus B here present in universal set but not in J means hus right a complement means what a complement means present in universal said but not in a.

[00:20:02]>> Yes sir.

[00:20:03]>> Got it.

[00:20:04]>> Yes sir.

[00:20:05]>> Sir your voice is not audible too.

[00:20:10]>> Audible sir >> present in universal set but not in a that is a complement. Got it?

[00:20:18]>> Yes sir.

[00:20:18]>> Yes sir.

[00:20:19]>> Yes sir.

[00:20:22]Example a = 1 2 3 universal set is equal to 1 2 3 4 right?

[00:20:39]>> Yes.

[00:20:39]>> Yes sir.

[00:20:42]>> A complement is equal to what is the formula? Universal set minus A. Right?

[00:20:47]>> Yes sir.

[00:20:48]>> Yes sir.

[00:20:48]>> What is universal set? 1 2 3 >> 1 2 3 4 - 1 2 3 >> 1 2 3 1 2 3 gets cancelled equal to >> four >> four >> right?

[00:21:03]>> Yes sir.

[00:21:03]>> Yes sir.

[00:21:04]>> Yes.

[00:21:06]>> Complement of A complement >> equals to four >> equals a complement complement universal set minus a complement.

[00:21:18]>> Right? What is universal set? 1 2 3 4 right >> and a dash is four.

[00:21:26]>> A dash is four.

[00:21:29]>> Present in A but not in >> 1 2 3 >> B >> 1 2 3 >> means what? It is equal to A only.

[00:21:38]>> Yes sir.

[00:21:39]>> Yes sir.

[00:21:39]>> Yes sir.

[00:21:41]>> Complement of A complement is equal to what? Complement of A complement is equal to a A.

[00:21:48]Right.

[00:21:49]>> Yes, sir.

[00:21:50]>> Yes, sir.

[00:21:50]>> See some more examples.

[00:22:05]What is set B?

[00:22:09]What is B= A C?

[00:22:13]>> Set consisting elements A C. Right. What is universal set?

[00:22:18]A B C D A B C D >> Find B complement complement of B complement.

[00:22:27]>> Right.

[00:22:28]>> Yes sir.

[00:22:29]>> Yes sir.

[00:22:31]>> Right. What is B complement by definition?

[00:22:34]>> Mus B >> new minus B.

[00:22:37]>> Mu minus B. What is Mu?

[00:22:40]A B C DU A C >> A B D >> That is B right.

[00:22:56]>> Yes sir.

[00:22:56]>> Yes sir. Yes sir.

[00:22:57]>> It is B complement of B complement.

[00:23:00]>> Mus Bus mu minus >> B dash or B dash right? B dash mu minus B dash right >> yes sir >> yes sir >> what is mu dash mu >> A B C D >> A B C D >> minus B D >> minus B D >> B minus >> B small letters here I have small letters BB cancel DD cancel what will get >> ital only right.

[00:23:43]>> Yes sir. Yes sir.

[00:23:46]>> Bash >> complement of complement is equal to B.

[00:23:50]>> B >> right?

[00:23:52]>> Yes.

[00:23:52]>> Yes.

[00:23:58]>> If A is any set complement of A complement equal to what?

[00:24:04]A >> complement of A complement equal to A. A >> right.

[00:24:11]>> Yes sir.

[00:24:11]>> Yes sir.

[00:24:12]>> Yes sir.

[00:25:07]Yes, read this question. A = A B C= B C D= B C D E the following A intersection B dash A - intersection B dash >> don't say that yeah complement of A union B A complement union B complement pronounce like that one complement of A union B. First one second one A complement union B complement. Third one we have to pronounce it as complement of A intersection B A intersection B.

[00:25:51]>> Fourth one we have to pronounce it as complement of A. A complement intersection B complement.

[00:25:58]Right?

[00:25:59]>> Okay sir.

[00:26:00]>> How to pronounce it? Read it. How to pronounce >> complement of A union B?

[00:26:05]>> A union B. A complement union B complement complement of A intersection B A complement intersection B complement >> right do it now >> write your conclusion >> okay I'm giving 5 minutes time write very Easy.

[00:26:35]>> Oh, yes.

[00:34:22]I think What?

[00:35:25]>> Huh?

[00:35:26]>> Sir, completed sir.

[00:35:29]>> Yes. Tell what is the result?

[00:35:32]>> Sir, first and second are same and third and fourth are same.

[00:35:37]>> Okay, let me check.

[00:35:43]What is the first one?

[00:35:45]How do I write?

[00:35:46]>> Union of A complement of A >> complement of A B.

[00:35:54]>> So find this one. What we have to find first?

[00:35:57]>> Sir, we have to find >> A union B first, right?

[00:36:02]>> Yes sir. This is this is nothing but universal set minus a >> minus a >> complement of a union b means what?

[00:36:10]Complement of a union b means universal set minus >> minus a union >> right? Yes sir.

[00:36:18]>> Directly I'm writing what is universal set >> a cus a union and b set a union and b set directly you write a >> a b c d >> b c d >> right difference a b c a b c d get cancelled >> set consisting the element e right >> yes sir sir first What is the second one?

[00:36:52]>> Compliment A union B >> A complement union B complement, right?

[00:37:00]>> Yes sir.

[00:37:07]>> What is A complement? First we find A complement.

[00:37:11]Universal set a >> U minus A is >> what is universal set? A B A B C D C D E >> What is A?

[00:37:26]>> A B C >> right?

[00:37:31]>> Yes sir.

[00:37:32]>> D E >> A B C A B C gets cancelled. Common >> D E.

[00:37:38]>> They are common elements. D right? Yes sir.

[00:37:42]>> Yes sir.

[00:37:44]>> What is B complement?

[00:37:47]Mus >> A B C D E >> A B C D E minus >> B C D >> is equals to A E >> common elements B C D B C D Right.

[00:38:10]>> Yes sir.

[00:38:11]>> A E sir.

[00:38:12]>> A E >> right?

[00:38:15]>> Yes sir. A complement union B complement.

[00:38:21]What is A complement?

[00:38:24]D E >> D E.

[00:38:27]>> What is B complement?

[00:38:30]>> A E.

[00:38:31]>> What you will get? A D >> A D E.

[00:38:35]>> Is it 182 or same?

[00:38:37]>> No sir.

[00:38:39]>> I not same.

[00:38:42]Right.

[00:38:43]>> Yes.

[00:38:44]>> Let me check. Let me check. Third one.

[00:38:48]What is third one?

[00:38:52]>> Complement of compment of >> A intersection B >> means what? This is equal to >> mus A intersection B.

[00:39:02]>> A intersection B.

[00:39:04]>> Very nice. Mu minus A intersection B.

[00:39:09]>> Universal set minus A intersection B.

[00:39:12]What is the universal set? A A B C D E >> minus what is A intersection B? Common elements in A and B.

[00:39:24]What are the common elements in A and B?

[00:39:26]>> BC B C right?

[00:39:30]>> Yes sir.

[00:39:30]>> Yes sir.

[00:39:31]>> Check A. A elements of A are A B C.

[00:39:34]Elements of B are B C D. B comma C are common elements in both A and B.

[00:39:38]Therefore >> Yes sir.

[00:39:39]>> Intersection means set of common elements in A comma B. Yes sir.

[00:39:44]>> BC right?

[00:39:46]>> Yes sir. E B C B C A D E >> I don't >> Sir and third are same.

[00:39:57]>> Second and third are same. Complement of A intersection B equal to A complement union Union B complement right?

[00:40:07]>> Yes sir.

[00:40:09]What is the fourth one?

[00:40:12]Sir, >> a complement intersection B complement.

[00:40:16]>> Right?

[00:40:18]Yes sir.

[00:40:19]>> What is a complement? How to write a complement?

[00:40:23]>> Mus E sir.

[00:40:28]>> Mu minus A. What is mu? A B C A B C D E.

[00:40:35]Right.

[00:40:36]>> Yes sir. minus >> a b c >> d e >> d e >> we compliment.

[00:40:50]>> Yes.

[00:40:53]A E sir, we already E sir.

[00:40:56]>> A E >> A B C D E once again we do. No problem.US B C D B C D A E >> right?

[00:41:14]>> Yes. A complnt intersection B complement >> D comma E intersection intersection A E >> the comp E >> sir first and fourth are same >> first and fourth are same first one set E fourth is also single element E first and fourth are same next third and second and third are same right >> yes sir >> yes sir >> what is Our conclusion complement of a union bal >> complement of A union B is equal to >> complement of >> complement of A B is equal to A complement intersection >> intersection B complement >> B complement >> union becomes intersection right?

[00:42:08]>> Yes sir.

[00:42:09]>> Yes sir. A intersection complement is equal to A complement only.

[00:42:17]These are called as Doron loss.

[00:42:21]>> What?

[00:42:22]>> These are called as Doron loss. D Morgan loss.

[00:42:27]>> Dor these are known as >> D Morgan laws.

[00:42:37]>> Doran laws. Complement of A union B is equal to A complement intersection >> B complement >> complement >> Complement of A intersection B equal to >> A complement >> A complement union B complement >> B complement right?

[00:42:53]>> Yes sir.

[00:42:54]>> Yes sir.

[00:42:55]>> Got it.

[00:42:56]>> Yes sir.

[00:42:57]>> Yes sir.

[00:43:07]Right.

[00:43:10]Next.

[00:43:25]Next concept is Subset.

[00:43:36]>> Subset.

[00:43:42]If a come only two sets, if a b two sets suppose let a b are any two sets if all if all the elements of A or elements of B then A is called as subset of B. A is called as >> subset of B.

[00:44:33]>> We denote it with This is the symbol for subset.

[00:44:48]>> Subset.

[00:44:49]>> Subset.

[00:44:50]>> Subset.

[00:44:51]>> Pronounce it as a subset.

[00:44:56]>> A subset B.

[00:44:57]>> A B.

[00:44:59]>> A subset of B. Right? How? We have to pronounce like that one. Read the definition.

[00:45:05]Let A two sets all the elements of A is called as subset of Bet. We denote it with weet subset of B.

[00:45:21]>> Right?

[00:45:23]If all the all the elements of A are in B, right?

[00:45:30]>> Yes sir.

[00:45:33]We say that A is subset of >> B.

[00:45:37]>> Right? Is it clear?

[00:45:39]>> Yes sir.

[00:45:40]>> Yes sir.

[00:45:59]Is it all the elements of A are in B?

[00:46:02]>> Yes sir.

[00:46:03]>> Yes sir.

[00:46:04]>> Clearly A subset for B or not?

[00:46:07]>> Yes sir.

[00:46:08]>> Yes sir.

[00:46:09]>> Is it all the elements of B are in A?

[00:46:11]>> No sir.

[00:46:12]>> No sir.

[00:46:13]>> Is it B subset of A?

[00:46:15]>> No sir.

[00:46:16]>> No sir. Here here A is subset for B but not B is subset for A right.

[00:46:21]>> Yes sir.

[00:46:22]>> Yes sir. Here >> a subset of B but not >> here this is this is called as I before that one I have to tell one symbol belongs one symbol notation otherwise this is the symbol belongs to >> belongs to.

[00:46:53]>> Yes sir.

[00:46:55]>> What is this symbol?

[00:46:57]>> Belongs to >> belongs to >> an element if a= set a b c. Here a belongs to a correct or not?

[00:47:09]>> Yes sir.

[00:47:10]>> Yes sir.

[00:47:11]>> A is an element of >> A belongs to A and B belongs to A. C belongs to >> A and C belongs to A.

[00:47:17]>> C belongs to A >> and D doesn't belongs to A. A is not in A.

[00:47:24]>> Yes sir.

[00:47:24]>> Yes sir.

[00:47:25]>> Not not this is the symbol for not. Not belongs to >> just cross it. Cross not cross it. Right symbol belongs to and cross mark. Put vertical cross. This is not belongs to right. Got it?

[00:47:37]>> Yes sir.

[00:47:38]>> Yes sir.

[00:47:40]>> This is what not >> equals to belongs to not belongs to >> right?

[00:47:47]>> Yes sir.

[00:47:48]>> Yes sir.

[00:47:49]>> B is not belongs to A. Right. A belongs to Aongs to A belongs to A right.

[00:47:54]>> Yes sir.

[00:47:57]A belongs to A only. Is it A belongs to B or not?

[00:48:02]>> Yes sir.

[00:48:04]>> B belongs to A >> and B belongs to A >> and B belongs to Bongs to B or not.

[00:48:11]>> Yes sir.

[00:48:12]>> Yes sir. Cong belongs to A and C belongs to B.

[00:48:19]>> B not belongs to B.

[00:48:21]for all the >> Okay sir.

[00:48:23]>> Every every each element of A is in B or not.

[00:48:26]>> Yes sir.

[00:48:27]>> Yes sir.

[00:48:29]>> Each element of A is in >> belongs to B.

[00:48:36]>> Hence A is subset for B. Right?

[00:48:40]>> Yes sir.

[00:48:41]>> Yes sir.

[00:48:42]>> A subset for >> B.

[00:48:45]Right. Clear.

[00:48:47]>> Yes sir.

[00:48:50]Is it B is subset for A?

[00:48:53]>> No sir.

[00:48:53]>> No sir.

[00:48:56]>> No reasonal >> because not present but not in A belongs to B but >> but not in A does not belong to A right.

[00:49:08]>> Yes sir.

[00:49:09]>> Yes sir.

[00:49:11]D belongs to B but D is not B.

[00:49:13]>> But D belongs to A.

[00:49:14]>> D does not belongs to A. Right.

[00:49:17]>> Yes sir. That is enough. A subset for B or not, right?

[00:49:21]>> Yes sir.

[00:49:22]>> A subset for B but is not subset for A.

[00:49:25]Right.

[00:49:26]>> Yes sir.

[00:49:27]>> Yes sir.

[00:49:35]>> Next Is is P subset for Q?

[00:49:58]>> No sir.

[00:49:59]>> No sir.

[00:50:00]>> No reason >> because two is not belongs to Q.

[00:50:06]>> Two belongs to P.

[00:50:08]>> Two belongs to B. But >> but not belongs to >> Q >> right?

[00:50:16]>> Yes sir.

[00:50:17]>> Therefore P therefore P is not subset for Q.

[00:50:22]>> Not subset >> Q.

[00:50:25]>> This is the symbol is what? Not >> not >> not subset.

[00:50:30]>> P is not subset for Q. Right.

[00:50:32]>> Yes sir.

[00:50:33]>> Yes sir.

[00:50:38]is Q is subset for P.

[00:50:40]>> No sir.

[00:50:42]>> Why belongs to Q?

[00:50:50]>> One element belongs to Q but not belongs to P.

[00:50:54]>> Five belongs to Q but not reason one element is enough. Five belongs to Q but but not belongs to Five not belongs to P >> right?

[00:51:11]>> Yes sir.

[00:51:12]>> Yes sir.

[00:51:13]>> Is it clear?

[00:51:14]>> Yes sir.

[00:51:15]>> Yes sir.

[00:51:33]>> Is A subset for X?

[00:51:35]>> Yes sir.

[00:51:35]>> Yes sir. Yes, every set is subset to itself only, right?

[00:51:40]>> Yes, sir.

[00:51:40]>> Yes, sir.

[00:51:48]>> A belongs to Amplies Aongs to A, right?

[00:51:51]>> Yes sir. Yes sir.

[00:51:53]>> Left side, right side, left side set, right side set side set side set side set side set side set side set side set side set side set side, right?

[00:51:58]>> No sir.

[00:51:59]>> A belongs to left side set side set implies A belongs to right side set side set. Right?

[00:52:03]>> Yes sir.

[00:52:05]>> Next. Next B belongs to left side set.

[00:52:09]>> B belongs to right belongs to right side set.

[00:52:14]>> C belongs to right belongs to left side set and C belongs to right side set right side set.

[00:52:20]>> Every element of left side left side set is >> is belongs to right side set.

[00:52:25]>> Right?

[00:52:26]>> Yes sir.

[00:52:29]Each element of left hand side set A is equal >> an element of right hand side set B. Right? B.

[00:52:45]>> Yes sir.

[00:52:46]>> Right hand set A. Right.

[00:52:51]Therefore A subset for A is right.

[00:52:56]Yes sir.

[00:52:57]>> What is our conclusion?

[00:53:00]>> Each element of >> each element of is belongs to >> that is okay. Conclusion is what? Every set is subset to >> itself.

[00:53:11]>> Itself.

[00:53:16]>> Every set is subset to itself here.

[00:53:19]>> Yes sir.

[00:53:20]>> Yes sir.

[00:53:21]>> Every set is subset to itself. Right.

[00:53:24]>> Yes sir.

[00:53:25]Right?

[00:53:27]Is it clear?

[00:53:29]>> Yes sir.

[00:53:29]>> Yes sir.

[00:53:31]>> Therefore B is any set. This B is subset for B. True or not?

[00:53:36]>> Yes sir.

[00:53:44]>> B subet to B is true, right?

[00:53:48]>> Yes sir.

[00:53:48]>> Yes sir.

[00:53:50]>> Next.

[00:54:07]is empty set is subset to 1, two. Is it true?

[00:54:11]>> No sir.

[00:54:12]>> Why?

[00:54:20]element present in empty set but not in right hand side.

[00:54:24]>> Yes. Yes.

[00:54:32]Right.

[00:54:37]You tell one element.

[00:54:39]>> You tell one element.

[00:54:43]I prove that right your argument is correct right.

[00:55:06]No sir.

[00:55:10]A cir is subset for Q.

[00:55:16]>> No sir.

[00:55:17]>> No sir. Why? Why P is not subset for Q?

[00:55:22]>> Two belongs to P.

[00:55:24]>> Two. No. No. Is it P is subset for Q?

[00:55:27]No.

[00:55:28]>> No. P is also not there. I >> P is subset. I am asking about P subset for Q. Oh okay sir. No sir P is not two belongs to P.

[00:55:41]>> Twongs to P two not belongs to that reason we can tell here.

[00:55:49]No sir no you cannot choose any element from empty set. Yes sir. That's why yes is true. S is true. Right.

[00:56:02]This is correct. This is correct. Right.

[00:56:05]Got it.

[00:56:06]>> Yes sir.

[00:56:08]>> Is empty set is subset for set 1 comma 2? What is your answer? Yes.

[00:56:13]>> Yes.

[00:56:14]>> Right. Therefore empty set is subset for every set.

[00:56:18]>> Yes sir.

[00:56:19]>> Yes sir.

[00:56:21]>> Empty set is subset for every set.

[00:56:28]>> Every set.

[00:56:29]>> Got it.

[00:56:30]>> Yes sir.

[00:56:32]If you take any any set empty set is subset for it itself is every set is subset to itself also right?

[00:56:41]>> Yes sir.

[00:56:42]>> Minimum minimum two subsets step got it.

[00:56:46]>> Yes sir sir I didn't understand sir.

[00:56:51]>> Yes. What is my question here? Is empty set is subset for 1a 2 unknown? What is your answer?

[00:56:58]>> Yes.

[00:57:07]If your argument is no reason to tell the reason one element in left hand side set and prove that it is not in right hand side set is it possible to you?

[00:57:22]>> No because it is that is not possible to you. That's why yes stands good.

[00:57:28]Okay sir.

[00:57:30]>> Understood?

[00:57:32]>> Yes sir.

[00:57:32]>> Yes sir.

[00:57:33]>> Why this yes stands good means? If you say it is no then you have to tell one reason. What is that reason? One element present one element present in left hand side set but it is not in right hand side set that you have to prove. Is it possible to you?

[00:57:49]>> Yeah.

[00:57:50]>> No, it is not possible to you. That's why >> because there is no element >> uh there is no element in left hand side. You cannot tell one element from left hand side set right?

[00:58:00]>> Yes sir.

[00:58:01]>> That is present in left hand side set but right but not in right hand side set that you cannot prove right there.

[00:58:08]>> Yes sir.

[00:58:08]>> Therefore my assumption stands good.

[00:58:11]What is my assumption? It is S. Got it?

[00:58:14]>> Yes.

[00:58:15]>> Yes sir.

[00:58:16]>> This is the proof for it. Therefore empty set is subset for >> every set.

[00:58:21]>> Every set. Any set you take empty set is subset for it. Right.

[00:58:25]>> Yes sir. Every set every set is subset to itself only right?

[00:58:29]>> Yes sir.

[00:58:30]>> Yes sir.

[00:58:30]>> Got it. Therefore >> yes sir >> empty set is subset to every set >> and it >> and itself every set. This is number one.

[00:58:48]>> Every set subset to itself itself >> right?

[00:58:54]>> Yes sir.

[00:58:57]Yes. Tell tell these two points.

[00:59:01]>> Every set itself to itself.

[00:59:07]>> Every set is subset to >> itself.

[00:59:11]>> Got it.

[00:59:12]>> Yes sir.

[00:59:13]>> Yes sir.

[00:59:22]Write all subsets of a set a b.

[00:59:37]What is given set?

[00:59:40]>> A equals to a comma b >> equals to a b.

[00:59:43]>> All subsets first set empty set. Empty set is subset to a correct.

[00:59:49]>> Yes sir.

[00:59:50]>> Yes sir.

[00:59:52]This is singleton A. Is it subset to A?

[00:59:56]>> Yes sir.

[00:59:57]>> Yes sir.

[00:59:58]>> Third one. Singleton B.

[01:00:03]>> It is subet. Correct or not?

[01:00:06]>> Yes sir.

[01:00:07]>> Yes sir.

[01:00:11]>> Final one in >> it is subset to itself.

[01:00:15]>> It Yes sir. Set a comma b.

[01:00:21]Got it?

[01:00:22]>> Yes sir.

[01:00:24]>> How many subsets exist for a set consisting two elements?

[01:00:28]>> Four subsets.

[01:00:29]>> Four subsets, right?

[01:00:32]Or >> yes sir.

[01:00:33]>> Yes sir.

[01:00:34]>> Or subsets of state a right.

[01:00:40]>> Yes sir.

[01:00:41]>> Yes sir.

[01:00:42]>> What is n of a? N of a is equal to two.

[01:00:46]Right. Yes sir. The elements in curve >> right number of number of subsets of elements >> number of subsets a equal to four.

[01:00:58]Right?

[01:00:59]>> Yes sir.

[01:01:00]>> Yes sir.

[01:01:01]>> N of a equal to two. Number of subsets of a equal to four. Right.

[01:01:05]>> Yes sir.

[01:01:09]>> Example. Another example.

[01:01:15]ABC. Write all subsets of B.

[01:01:29]>> First subset empty set. Correct.

[01:01:31]>> Empty set.

[01:01:32]>> Yes sir.

[01:01:32]>> Yes sir.

[01:01:33]>> Second subset B2.

[01:01:35]>> A belongs to B.

[01:01:37]>> Singleton B.

[01:01:38]>> A belongs to B.

[01:01:40]>> Singleton B >> and C's belongs to B. Single Congs and B C A.

[01:01:54]>> Yes, sir.

[01:01:55]>> Two elements. One element sets over. No element set.

[01:01:59]>> One element set. Two element sets.

[01:02:02]>> Yes, sir. C, C. Right.

[01:02:07]Yes sir.

[01:02:07]>> Then AB and A >> ABC means B itself, right?

[01:02:19]>> Yes sir.

[01:02:20]>> How many subsets are possible for real?

[01:02:22]>> Yes sir.

[01:02:23]>> Yeah.

[01:02:26]Yeah.

[01:02:35]of B = 3 implies >> number of subsets >> number of subsets of B = 8 >> right >> yes sir >> next one I'm writing the next one N of C is equal to 4 >> then >> number of subsets If you write >> number of subsets of C is equal to 16.

[01:03:09]>> Yes sir. Because >> four 2= 8 right?

[01:03:17]>> Yes sir.

[01:03:17]>> Yes sir.

[01:03:18]>> 2 2= 4 right here.

[01:03:21]>> Yes sir. 2= 8 = 4 2 = 8 >> 2 4 = 16 = 16 write a result number of a = m n then number of subsets of a equal to two power N >> got it.

[01:03:53]>> Yes sir.

[01:03:54]>> If set A has n elements then number of subsets for A is two power >> N.

[01:04:01]>> Right. Got it.

[01:04:03]>> Yes sir.

[01:04:17]Number of subsets of a= >> 32 sir 2 ordinal number of a >> 2^ 52 >> is equal to 3 >> 32 >> 32 >> you will get 32 subsets.

[01:04:36]>> Yes sir.

[01:04:37]>> Yes sir.

[01:04:38]>> Got it.

[01:04:39]>> Yes sir. Sir.

[01:04:41]>> Yes. Today we discussed about complement of a set.

[01:04:46]>> Complement of a set and subset. Right?

[01:04:48]>> Yes sir.

[01:04:49]>> Yes sir.

[01:04:50]>> Complement of a set means present in universal set but not in that set as complement not in that set.

[01:04:56]>> Right?

[01:04:57]>> Yes sir.

[01:04:57]>> Yes sir.

[01:04:58]>> Complent complement of a set means present in universal set but not in that set is called as complement of the set.

[01:05:03]Right?

[01:05:04]>> Yes sir.

[01:05:04]>> Yes sir.

[01:05:05]>> A is any set. A complement is nothing but universal set minus A. Right.

[01:05:10]>> Yes sir.

[01:05:12]>> What is the result? Complement of a complement is equal to complement of a complement is equal to itself only a only right?

[01:05:22]>> Oh yes sir.

[01:05:23]>> Yes sir.

[01:05:24]>> Complement of complement of a complement is equal to a another 2D more than loss.

[01:05:30]Complement of A union B is equal to >> A complement intersection B complement >> B complement >> complement >> complement of A union B is equal to A complement >> A complement intersection B complement of complement of A union B is equal to A complement intersection B complement complement of A intersection B equal to A complement union B complement right >> b complnt yes sir >> union becomes intersection and intersection becomes Similar results we have observed in difference of sets also. A minus of B union C is equal to A minus B intersection A minus C. They are similar to distributive property but not distributive right.

[01:06:17]>> Yes.

[01:06:19]Similar the type of similar but symbol is changing in distributive symbol not changes. Oh sir right. symbol not changes in distributive property but similar type of property right >> yes sir >> yes sir >> okay these are the important things we'll end in sets right on the notes not last right >> yes sir yes sir >> okay bye >> bye bye