Day 26 - CRACK SSC MATHS by DEO, Nizamabad Sri P.Ashok garu

Ajouté : 2026-05-26

[00:03:38]I for >> good morning sir.

[00:03:43]>> Good morning.

[00:03:48]>> Sm first step.

[00:03:51]>> No no no sin square theta plus fourth fourth and fifth set.

[00:03:56]Sin square theta + sin square theta= 1 square= 1 - cos² theta square theta= 1 - sin square theta then cos x² theta - square theta = 1 cos x square theta = 1 square theta = cos x square theta - 1 square tan square theta = 1 square theta = 1 square theta = 1 + tan tan square theta tan square theta = square theta - 1. Then se square theta + tan square theta into se square theta tan square theta = 1 theta + tan theta into se theta + tan theta into se theta tan theta = 1 theta tan theta = 1 theta + tan theta or se theta tan theta = 1 theta + tan theta then cos x² theta cosec theta minus co theta into cosec theta + theta = 1 cosec theta + theta or cosec= 1x cosec theta theta >> correct public tell the points of set a set is a collect uh uh collection of well design defined objects.

[00:06:11]>> A set contains elements. The set contains elements. Uh there are three types of sets.

[00:06:20]>> Infinite set uh uh finite set and uh empty set.

[00:06:28]>> Infinite finite set means uh a set which has countable elements. Infinite set mean >> fixed number of elements.

[00:06:40]>> Uh infinite set means a set which has uh not fixed elements. We can we can't count them.

[00:06:50]>> Uh empty set means a set which which doesn't have any element.

[00:06:56]>> Uh cardial number. Cardial number means the number of elements present in a set is known as cardinal number.

[00:07:07]Uh >> Union.

[00:07:29]Okay.

[00:07:34]What is it?

[00:07:55]Hello.

[00:07:56]>> Hello. Yes sir. Union of two sets >> sir. Uh if A and B are any two sets then union of A and B is denoted with A union B >> right?

[00:08:16]>> And defined as collection of all elements of A and B.

[00:08:20]>> Right.

[00:08:22]Elements of elements of sets elements of sets are written with small letters. Uh >> elements of sets are written with small letters. Uh the name of set is written with capital letter.

[00:08:38]>> Right? We list all the we write all the elements of the set we separated with commas and put in bracket. Right? H >> in a curve bracket.

[00:08:48]>> Right.

[00:08:50]Right. That is actually order is not important not important in writing elements.

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

[00:08:59]>> Order is not important. I uh >> Repetition is not not repetition is not necessary right?

[00:09:08]>> Yes sir.

[00:09:10]>> Is not necessary right?

[00:09:12]>> Yes sir. Repetition is not necessary.

[00:09:15]Okay.

[00:09:25]It's been Okay.

[00:10:28]We discussed about union of two set right?

[00:10:31]>> Yes sir.

[00:10:33]>> How to write a union and b write all the elements of a and write all the elements of b >> elements of b.

[00:10:39]>> Then we will get a union and set right.

[00:10:41]>> Yes sir.

[00:11:01]A= ABC.

[00:11:09]>> What you will get?

[00:11:11]>> ABC.

[00:11:12]>> ABC. Sir, >> ABC. Union >> ABC. A B C >> write all the elements of A and all the elements of A >> elements of B. We not need repeatation.

[00:11:25]So ABC >> therefore A is equal to A.

[00:11:33]>> This is called as important property as properties of union.

[00:11:51]Number one, commutative property.

[00:11:59]>> A union B is equal to >> that is called asative property. Right?

[00:12:07]>> Yes sir. Next associative property.

[00:12:17]A union of B is equal to A >> see A union of B union C equal to A union B union C. This we proved right?

[00:12:30]>> Yes. Yes sir.

[00:12:33]>> Identity property union empty setal empty set union= right. Yes sir.

[00:12:47]>> That is identity property and important property right.

[00:13:03]>> Yes sir.

[00:13:09]>> Got it.

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

[00:13:12]>> Next.

[00:13:19]Intersection of >> What is the next concept?

[00:13:27]>> Intersection of two sets.

[00:13:29]>> Two sets.

[00:13:30]>> Two sets.

[00:13:33]A comma b any two sets.

[00:13:39]Then their intersection intersection of A is denoted with A section B.

[00:14:04]This is inverted U right?

[00:14:06]>> Okay sir.

[00:14:09]inverted U. That is the symbol intersection A intersection of B.

[00:14:14]>> How to read?

[00:14:16]>> A intersection B.

[00:14:19]>> A intersection of B. A intersection B.

[00:14:21]Right.

[00:14:23]>> Yes sir.

[00:14:23]>> Yes sir.

[00:14:25]can be defined as as the set of all common.

[00:14:40]Set of all common elements of a comma bir.

[00:14:44]>> Got it.

[00:14:45]>> Yes sir.

[00:14:46]>> Yes sir.

[00:14:46]>> Yes sir.

[00:14:47]>> The set of all common elements of a comma b is denoted with a intersection b. Got it?

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

[00:14:55]>> Say the example.

[00:15:00]>> 1 2 3 B = 2 3 4 Action.

[00:15:14]What is it?

[00:15:16]1 2 3.

[00:15:18]>> What is it? 2 3a 4 >> which are common elements >> 2 and 3 2 and three and 2 3 are common elements right?

[00:15:31]>> Yes sir.

[00:15:32]>> Set consisting set consisting these common elements is called as a intersection b. Got it?

[00:15:38]>> Okay sir. Yes sir. Yes sir. That 2 3 is a intersection b. Got it?

[00:15:44]>> Yes sir.

[00:15:44]>> Yes sir.

[00:15:49]Point number one, B intersection. Number two, B intersection.

[00:15:53]What is B intersection?

[00:15:56]First you have >> 2a 3 2a 3 3a 4 intersection of 1a 2a 3 >> 1 2a 3 >> 1 2a 3 >> which is common intersection is also 2a 3 >> A intersection B and B intersection is same or not.

[00:16:20]>> Yes sir.

[00:16:22]Therefore, Action Balction is committed to >> Yes sir.

[00:16:38]>> property, right?

[00:16:41]>> Yes sir.

[00:16:42]>> Intersection is got it >> sir.

[00:16:49]Perfection means set of proper elements only right?

[00:16:52]>> Yes sir.

[00:16:53]>> Yes sir.

[00:16:55]>> Example P intersection.

[00:17:18]What is intersection Q?

[00:17:20]>> A B C A B C D C D >> intersection intersection A D F A F A F A F A F A F A F A F A F A F A G A D F G >> A F G >> What are the common elements?

[00:17:38]>> A and D A is common and D is common, right?

[00:17:42]>> Yes sir. Yes sir. It is nothing but a d intersection.

[00:17:48]>> Yes.

[00:17:49]>> Got it.

[00:17:50]>> Yes sir.

[00:17:51]>> Yes sir.

[00:17:53]>> This is the concept of intersection. It is set up on common elements only.

[00:17:56]Right.

[00:17:58]>> Yes sir.

[00:18:07]How many members understood this intersection concept? Please raise your hand.

[00:18:26]She's already No question about this.

[00:19:11]Please cohost me sir.

[00:19:14]>> Who sir?

[00:19:17]>> Okay.

[00:19:24]>> Thank you sir. Right.

[00:19:47]Yes.

[00:19:51]>> Yes. Got it. Is it my screen? My screen is visible.

[00:19:55]>> Yes sir.

[00:19:55]>> Yes sir. Yes sir.

[00:19:57]>> Is very simple concept, right?

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

[00:20:32]Yes. Read the question.

[00:20:34]A = 1A 2a 3 = 2 2a 3a 4a 5 = 3a 5a 6 find a union b a union of b union >> it is not union it is not union intersection a intersection of b intersection c uh b a intersection of >> intersection of B intersection C.

[00:21:06]You have to read it as A intersection of B intersection C. Second one is A intersection B of intersection C.

[00:21:14]>> Intersection C. Right? First one check A intersection of B intersection C. To find that one, what do I have to find? B intersection C. We have to find, right?

[00:21:26]>> Yes, sir.

[00:21:27]>> Yes. H.

[00:21:28]>> How to write? What is B? 2a 3 intersection. What is 3a 5?

[00:21:41]>> What are the common elements?

[00:21:43]>> 3a 5 >> 3a 5 common elements, right?

[00:21:48]>> Yes sir.

[00:21:50]>> Two intersection is 3a 5. Right?

[00:21:52]>> Yes sir.

[00:21:53]>> Yes sir.

[00:21:55]>> Intersection C is 3a 5. Right?

[00:21:57]>> Yes sir.

[00:21:58]>> Yes sir.

[00:22:00]Next. A intersection.

[00:22:04]What is set A >> B intersection C?

[00:22:13]>> 3 5 >> 3 is the common element, right?

[00:22:27]>> Yes sir. A intersection of B intersection C is three, right?

[00:22:31]>> Yeah.

[00:22:34]>> This is A intersection of B intersection C. First one.

[00:22:38]>> What is the second one? A intersection B of intersection C.

[00:22:44]>> What do I have to find first?

[00:22:46]>> A intersection B.

[00:22:49]>> What is A intersection A? Set 1 2 3.

[00:22:52]Right?

[00:22:53]>> Yes, sir.

[00:22:53]>> Yes, sir.

[00:22:55]>> What is B?

[00:22:58]43 right?

[00:23:01]>> Yes sir.

[00:23:02]>> Yes sir.

[00:23:06]>> What are the common elements?

[00:23:08]>> 2 and three are common elements.

[00:23:09]>> 2 and three are common elements.

[00:23:13]>> 2 and 3 = 2.

[00:23:16]>> A intersection B intersection C.

[00:23:19]>> What is the intersection B? 2A 3. Right.

[00:23:22]>> 2A 3.

[00:23:24]>> What is C? intersection 3A 5 >> 3a 5a 6 >> 3a 5a 6 right >> yes sir >> yes sir >> yes what are the common elements >> only common element >> intersection equal to three >> same or not both of them are same or not >> yes sir yes sir >> what is your our conclusion a intersection Yes. Associative, right?

[00:24:07]>> Yes. Yes, sir.

[00:24:08]>> Yes, sir.

[00:24:11]>> Associative.

[00:24:13]>> Associative.

[00:24:26]Intersection of sets is associative right? Associate.

[00:24:32]>> Yes sir. Yes sir.

[00:24:53]I'm not sure.

[00:24:55]>> Yes, sir.

[00:24:56]>> Yes, sir.

[00:24:57]>> Good night.

[00:25:17]Wait for one minute.

[00:25:30]>> Thanks.

[00:25:57]What is the definition? Next definition is >> universal set.

[00:26:03]>> Universal set.

[00:26:11]>> Universal set.

[00:26:15]is the comprehensive collection of comprehensive collection of >> all elements relevant to particular ular situation, particular contest or situation.

[00:26:58]>> As what is the definition of universal set?

[00:27:01]>> Universal set is the comprehensive collection of all elements relevant to the particular context.

[00:27:12]context or situation anything you can write.

[00:27:17]>> Okay.

[00:27:18]>> It is denoted with >> mu that set is denoted with >> mu >> mu that is un universal set mu universal set mean it collects all elements relating to a situation right?

[00:27:44]>> Yes sir. Yes sir. H for example.

[00:27:53]Example set is students of >> JPHS bin. What is it?

[00:28:13]>> Student of JPHs.

[00:28:19]set B is >> students of NPHs knowledge.

[00:28:30]What is NB?

[00:28:32]>> Students of JPs.

[00:28:36]>> We have these two these two sets. One is set students of Ben. Set is >> students of universal.

[00:29:01]>> Okay sir.

[00:29:02]>> Nip mandal covers binola and knowledge or not.

[00:29:05]>> Yes sir.

[00:29:06]>> Yes sir. Perfect model students means it includes it includes knowledge for this one access universal set all right.

[00:29:14]>> Yes sir.

[00:29:15]>> Yes sir.

[00:29:16]>> Any big set also you can take students of then also it acts as universal set right?

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

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

[00:29:23]>> Students of cover these two schools or not?

[00:29:26]>> Yes sir. Yes sir.

[00:29:28]>> Otherwise students of Telangan also universal set right?

[00:29:32]>> Yes sir.

[00:29:34]particular situation collecting all the elements of that particular situation is called as universal set. Got it?

[00:29:42]>> Yes sir.

[00:29:43]>> Yes sir.

[00:29:44]>> Is it clear?

[00:29:45]>> Yes sir.

[00:30:16]Is it clear? Set A is what?

[00:30:19]>> A B C >> A B C >> corresponding to this set. This one is universal set. Is it? Is it correct?

[00:30:25]>> Yes sir.

[00:30:26]>> Yes sir.

[00:30:29]This is your >> Yes sir.

[00:30:31]>> Yes sir.

[00:30:32]>> Yes sir.

[00:30:44]>> A intersection m intersection >> intersection.

[00:30:49]Uh what is intersection section A B C D C D E >> What you will get?

[00:31:04]>> A B C >> A B C >> ABC Sir ABC.

[00:31:11]>> Yes sir.

[00:31:12]>> Yes sir.

[00:31:15]Intersection is equal to only right only right?

[00:31:21]>> Yes sir.

[00:31:24]>> Number two intersection A intersection.

[00:31:29]>> What is >> A B C D A B C D E intersection A B C >> What do you get? What are the common elements? A B A B C >> Yes sir.

[00:31:43]>> A B C >> A B >> This is also equal to A only right?

[00:31:48]>> Yes sir.

[00:31:50]>> Therefore intersection = m= >> identity identity >> identity >> with respect to intersection.

[00:32:11]We access identity with respect to intersection. Right?

[00:32:15]>> Yes.

[00:32:16]>> In multiplications. In multiplication 2 into 1= 2 or not?

[00:32:21]>> Yes sir.

[00:32:21]>> 5 into 1= 5. Right? 5 into 1= 5. 1 acts as multiplicative identity.

[00:32:28]Right?

[00:32:30]>> Yes sir.

[00:32:31]>> In the before one empty set acts as identity.

[00:32:35]>> Addive identity.

[00:32:36]>> Huh. uh with respect to union. Empty set access identity with respect to union.

[00:32:42]>> Okay sir.

[00:32:44]>> Right. Universal set as university with respect to intersection.

[00:32:51]Right.

[00:32:53]>> Yes sir.

[00:33:34]Universal set.

[00:33:36]Please tell. 1 2 3 4 >> 1 2 3 4 5 6 7 >> 3 4 5 6 7 >> 1 2 3 4 5 6 7 >> 8 >> 1 2 3 4 5 6 7 8 9 right this one. Access access >> universal set.

[00:33:54]>> Universal set as universal set for >> context.

[00:34:05]Context right? Is it is it collecting all these cont?

[00:34:12]>> Yes sir.

[00:34:17]>> This action universal got it.

[00:34:20]>> Yes sir.

[00:34:22]>> Right.

[00:34:29]What is it?

[00:34:41]>> A intersection A is equal to what intersection itself only right?

[00:34:51]>> Yes sir.

[00:34:54]37.

[00:35:02]>> Yes sir.

[00:35:04]>> 13 57 5 >> Yeah.

[00:35:09]>> A intersectional >> A intersection A equal to >> A.

[00:35:17]Therefore intersection is >> very important.

[00:35:23]Identity.

[00:35:24]>> Identity >> intersection is important property. This is >> important >> important property right?

[00:35:32]>> Yes.

[00:35:34]>> Yes. What are the properties? Properties of intersection.

[00:35:43]Properties of intersection. Number one commutative property.

[00:35:51]What is commutative property? A intersectional >> B intersection A.

[00:36:00]>> Right.

[00:36:01]>> Okay.

[00:36:02]>> Yes sir.

[00:36:03]>> Second one. Associative property.

[00:36:09]What is associative property?

[00:36:11]A intersection of B intersection C is equal to >> A intersection B of intersection C >> right?

[00:36:21]>> Yes.

[00:36:22]>> Third one is identity property.

[00:36:29]>> What is identity property?

[00:36:33]A intersection is equal to intersection A= A.

[00:36:41]Mu acts as identity.

[00:36:44]>> Identity >> element >> element >> with respect to inter >> with respect to intersection >> identity set >> with respect to intersection.

[00:37:03]>> Right. Access identity set with respect to intersection. Got it.

[00:37:08]>> Yes sir. Fourth one is add important propert.

[00:37:26]>> Yes sir.

[00:37:26]>> Yes sir. Read these results. Read these results.

[00:37:31]>> Communative property A intersection B is equals to B intersection A. Associative property A intersection of intersection C= A intersection B of intersection C additive property the intersection mu = mu intersection A= A set important important property intersection A= Hey, wait.

[00:38:42]I'm not Yes, read it. Read the question.

[00:39:07]A= = A B C B = B C D C = C E find A intersection C A and B of section A C >> union A next intersection of B union C >> A intersection B union of A intersection >> C >> right?

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

[00:39:46]>> Very simple one. Let find it. What is the number one? A >> union B intersection C.

[00:39:56]>> First we have to find B intersection C.

[00:39:58]Right?

[00:39:59]>> Yes sir.

[00:40:00]>> What is B?

[00:40:01]>> B C D. B C D C D E C E >> C is the common element.

[00:40:15]>> C is a common >> C is the common election is there right? Only C right.

[00:40:25]>> Yes sir.

[00:40:26]>> Yes sir.

[00:40:28]>> A union of B intersection P right? Yes sir.

[00:40:34]>> A B ABC union of >> C >> A B C >> A >> ABC Ca C means it is nothing but >> the repetition is >> repetition is not >> necessary. Yes, necessary. Union means collect all the elements of the set and collect all the elements of all the elements of this set.

[00:41:01]>> This is nothing but not necessary. ABC right?

[00:41:05]>> Yes sir.

[00:41:07]>> Okay sir.

[00:41:08]>> Number one.

[00:41:10]What is the second one?

[00:41:12]>> A intersection >> intersection of A C >> A union B intersection A C. First what we have to find >> a union b we have to find what is a >> c right?

[00:41:37]>> Yes sir.

[00:41:38]>> Union B.

[00:41:45]>> Yes sir. B C D >> A union B set A B C Union set B. Right.

[00:41:51]>> Yes sir.

[00:41:52]>> What is What about this one? A B A B B B B B B B B B B B B B B B B B B B B B C C D C D C D Yes sir.

[00:42:02]>> Here operation is union means collect all the elements, right?

[00:42:06]>> Yes sir.

[00:42:08]>> Okay. This not necessary directly.

[00:42:10]directly you can write uh >> A B C D A B >> A B C D X >> A union C is equals to A C right >> yes sir >> uh what you will get directly I'm writing >> A B C E C E >> Right. Repetition is not necessary. A B C is right.

[00:42:44]>> Yes.

[00:42:46]>> Next intersection intersection of >> A union B intersection of union C.

[00:42:55]>> A union Bal A B C D E.

[00:43:07]>> Right. A B Circ from one to same or not?

[00:43:21]>> Yes sir.

[00:43:23]>> From one A union B inter is ABC, right?

[00:43:27]>> Yes sir.

[00:43:29]>> From two also it is ABC right?

[00:43:32]>> Yes sir. From 1 and two we conclude that we >> intersectional >> A union B intersection A >> A union C >> right?

[00:43:51]>> Yes sir. This property is called as >> distributive property of union.

[00:44:06]>> Distributive.

[00:44:08]>> Distributive property of union over intersection.

[00:44:12]>> Union over inter. Distributive property of union >> over >> over intersection >> over >> intersection >> intersection >> distributive property of union >> over intersection right this is called as distributive property right >> yes sir sir >> in numbers also we have 2 * of 3 + 5 how to write we write it as 2 * 3 + 2 * >> 5 sir Yes sir.

[00:44:44]>> 2 * 3 + 5. We can write it as 2 * 3.

[00:44:48]>> 2 * 3 + 2 * >> right in algebra also we do x * of y + how to write x into y >> x * of y + x * x * >> right?

[00:45:01]>> Yes.

[00:45:03]>> This property is called as distributive property of distributive property over addition.

[00:45:08]>> Yeah.

[00:45:09]This property is called as multip distributive property of multiplication over >> over addition property.

[00:45:18]Distributive property of union over >> over intersection >> intersection.

[00:45:22]>> Okay.

[00:45:23]>> Right.

[00:45:24]>> Yes.

[00:45:24]>> Yes sir.

[00:45:28]>> Got it.

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

[00:45:31]>> First time and second over. Third one is what?

[00:45:35]Intersection intersection B union A intersection C.

[00:45:41]>> First third one we have to prove >> intersection of B union C. Yes.

[00:45:48]>> What do we have to find first?

[00:45:49]>> C.

[00:45:53]What is set B?

[00:45:55]>> A B C D.

[00:45:56]>> No. What is B? Set. Check. B C D.

[00:46:01]B set C. C E. Right.

[00:46:07]3 CD C Dun C Ess C D E Right.

[00:46:34]Yes sir. Yes sir.

[00:46:36]>> Next. A intersection of B union say A B C intersection intersection B C D E right >> sir B sir.

[00:46:53]>> What are the common elements?

[00:46:55]>> B operation intersection right?

[00:47:00]>> Yes sir. Since intersection is there, you take only common elements, right?

[00:47:04]>> Common elements. Yes, sir.

[00:47:08]>> BC >> BC right?

[00:47:11]>> Yes sir. Yes sir.

[00:47:12]>> Is it clear?

[00:47:14]>> Yes sir.

[00:47:15]>> Very simple. Very simple. This one is equation number three.

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

[00:47:21]>> Which one is what? A intersection B.

[00:47:24]>> A intersection B.

[00:47:25]>> A intersection B union A intersection C.

[00:47:29]>> Right.

[00:47:31]First what we have to find >> A intersection B intersection B >> A intersection B right >> yes B A B A B C >> intersection intersection B >> B C D B B B B B B B B B B B B B B B B B B B B C D B C D B C D What are the elements? BC B B C Yes sir.

[00:48:07]A union C A inter >> A intersection A intersection C A B C >> A B C >> A B C >> Inter Cir.

[00:48:23]Yes sir.

[00:48:24]>> What are the common elements? C >> only right.

[00:48:29]>> Yes sir.

[00:48:30]>> Yes sir.

[00:48:36]>> Right. Yes sir. Intersection B >> A intersection >> intersection B union intersection C= >> is equals to C B C >> Union C is equals to B C B C >> Yes. Number four. Three and four are same.

[00:49:02]>> Yes sir.

[00:49:03]>> What is three? A intersection intersection B union A intersection C is equal to B C.

[00:49:15]>> Yes sir.

[00:49:17]>> Both of them are same from >> sir. We conclude that.

[00:49:29]A intersection of B union C is equal to >> A intersection of B union C.

[00:49:39]>> A intersection >> C.

[00:49:44]Yeah. Yes sir.

[00:49:45]>> This is called as what? This property is known as >> distributive property. Distributive property.

[00:49:50]>> This intersection over union.

[00:49:53]This property >> property >> called as >> known as >> called known as distributive property of >> union >> intersection over add over union >> distributive property of union >> inter union over >> intersection over >> of intersection over union.

[00:50:22]Got it.

[00:50:23]Yes sir.

[00:50:25]>> Distributive property of intersection over union. Right.

[00:50:31]>> Yes sir. Yes sir.

[00:50:32]>> This is sir.

[00:50:34]These are the properties. Right.

[00:50:37]>> Yes sir.

[00:50:39]>> Therefore distributive properties.

[00:50:48]What is the first one?

[00:50:51]A union of B intersection C.

[00:50:55]>> Yes sir. A intersection of >> A intersection A intersection U >> A intersection B of union of A intersection CB.

[00:51:22]of >> intersection >> intersection A union C right >> yes sir yes sir >> second one is >> A intersection >> A intersection >> B union B union C is equals to A intersection B union A intersection C >> right >> yes sir this is called distributive properties right?

[00:51:53]>> Yes sir. Yes sir.

[00:51:54]>> You are you are perfect in line and intersection right?

[00:51:58]>> Yes sir sir.

[00:52:00]>> One minute.

[00:52:01]>> Yes sir.

[00:52:09]>> How many members understood this union and intersection concepts? Please raise your hand.

[00:52:29]Very good. Many many students got it right.

[00:52:45]>> Very nice.

[00:52:50]Let move for other concept.

[00:52:53]>> Yes sir.

[00:52:55]Right.

[00:53:21]difference of two threads.

[00:53:23]>> Okay.

[00:53:24]>> What is the next concept?

[00:53:27]difference of two sets.

[00:53:44]If we are any two sets then different set That different set is denoted with a minus b.

[00:54:27]And the set of elements in but not in the definition. Ready?

[00:54:52]If a and b are two sets then different set of elements in present in elements present in a but not in yes elements it is a minus b is a new set right?

[00:55:23]>> Yeah.

[00:55:23]>> Yes.

[00:55:25]>> Difference set we call right.

[00:55:28]>> Yes sir.

[00:55:29]>> How how we are differing elements present in A but not in >> but not in B.

[00:55:35]>> Right.

[00:55:36]>> Yes sir.

[00:55:37]>> Yes sir. Give me one example.

[00:55:59]Let's read the question.

[00:56:15]A = A B C D = B E F >> A minus B >> A minus B uh B minus C >> B minus A.

[00:56:32]>> Yes. A - B C A B C D C F.

[00:56:48]>> Yeah.

[00:56:50]>> What is the A minus B set present in A but not in B?

[00:56:55]>> Present in B.

[00:56:59]element and >> B and D present in both or not?

[00:57:09]>> Yes sir. Yes sir.

[00:57:10]>> Present in A but not in B and M.

[00:57:14]>> A and C A and C that's only present in A but not in only right. Yes sir.

[00:57:26]Right.

[00:57:33]Choose that one. Bi is it in B or B? It is also in B or not.

[00:57:41]>> Yes sir.

[00:57:41]>> Yes sir.

[00:57:42]>> You leave it. You don't take that B. C present in A. But is it in B?

[00:57:48]>> In B >> but not in B.

[00:57:50]>> But not in B. That you can select C. But D. A and B and right.

[00:58:01]>> Yes sir.

[00:58:03]The elements only present in A but not in B.

[00:58:07]>> Elements cancelation common elements cancel elements they are a minus right?

[00:58:14]>> Yes sir. Yes sir. Yes sir. Yes sir.

[00:58:18]>> B minus A means first write B.

[00:58:21]>> Yes sir. B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D D E E F B D E F E Finus A D >> elements, right? B elements >> elements common elements, right? EU s these two are equal.

[00:58:52]>> No sir.

[00:58:54]>> Is it A minus B and B minus A are same?

[00:58:57]>> No sir. No sir. No sir. Earier A union B and B union are same. A intersection B and B intersection A are same. But is it A minus B and B minus A are same? No siral.

[00:59:10]What do we conclude?

[00:59:12]A not= minus a.

[00:59:17]>> Therefore, difference of sets not satisfies a communive property. Right?

[00:59:22]>> Yes, sir.

[00:59:23]>> Yes, sir.

[00:59:24]>> Difference of sets >> not satisfy commutative property.

[00:59:28]>> Not satisfies >> commitive property.

[00:59:31]>> Commutative property.

[00:59:37]Right. Got it.

[00:59:39]Yes sir.

[00:59:40]>> Yes sir. That is difference of two sets.

[00:59:42]Is it clear?

[00:59:44]>> Yes sir. Yes sir.

[01:00:13]Directly, what is P minus Q?

[01:00:18]>> 1 2 3 1 2 3 4 1 2 3 5 >> Direct answer 1.

[01:00:29]No problem. 1 2 3 5 rightus >> 2 3 4 5 >> 2 3 4 5 7 >> is equals cancel 1 >> 5 right >> yes sir >> what is Q >> - r 4a 7 >> sir 4a 7 >> 2a 3a 4 >> 3a 4a 7 - >> that's 1a 2 3 9 10 1 2 3 2 3 9 2 >> Right.

[01:01:12]>> Yes. Yes sir.

[01:01:14]>> 2 3 = 2a 7.

[01:01:22]>> This is nothing but 4a 7.

[01:01:26]>> Yes, sir.

[01:01:27]>> Is it clear? Yes sir. This is this is the what is RUS >> 1 2 3 >> R positive right or 2 3 9 10 >> Okay sir 2 3a 2 9 10 9 10 >> 10 1 2 3 1 2 3 cancel 9 10 9 N >> right.

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

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

[01:02:02]>> That is R minus P right?

[01:02:05]>> Yes sir. Yes sir.

[01:02:07]>> This is M. What is difference of two sets?

[01:02:10]>> Yes sir. Yes sir.

[01:02:12]>> It is not associative right?

[01:02:14]>> Yeah.

[01:02:15]>> Yes sir.

[01:02:49]Okay. Okay.

[01:03:14]You like that?

[01:03:30]It's not working.

[01:03:33]>> Okay. Say example.

[01:03:36]>> Okay.

[01:04:36]Read the question.

[01:04:49]A = >> 1 2a 3 B = 1A 2A 3 B = 2 3A 2 3 3A 7 C = 3A 5A 6A 7 A - C A B of union of A - C A intersection section A - Intersection of a minus a minus c.

[01:05:23]>> Right?

[01:05:25]>> Yes sir.

[01:05:26]>> How to find the first one? How to find the first one?

[01:05:29]>> We have to find we should c right?

[01:05:36]>> Yes sir.

[01:05:36]>> Yes sir.

[01:05:37]>> Then you should find a minus b union c.

[01:05:39]Right?

[01:05:40]>> Yes sir.

[01:05:41]>> Then how to find second one?

[01:05:44]So first we have first we should find a minus c then we should >> right second one is over third one how to find third one >> first we should find B intersection C next then you find a minus of B intersection C >> right how to find a minus B and A minus C. Then we should find AUS B of >> intersection of A minus C.

[01:06:20]>> Correct.

[01:06:22]>> Okay. Can you do this one? Homework.

[01:06:24]This one.

[01:06:24]>> Okay sir.

[01:06:25]>> Yes sir.

[01:06:26]>> This one is homework. You try it >> and Okay sir. Write the conclusion.

[01:06:32]>> Okay sir. Okay sir.

[01:06:34]>> What is your conclusion? After finding the finding these values you write the conclusion, right?

[01:06:40]>> Okay sir. Okay sir. Which which are equal? Which are which are equal? You can write it. Okay.

[01:06:46]>> Okay. Okay.

[01:06:47]>> Right. This is homework.

[01:06:50]>> Okay. Bye. Not down note down all these notes clearly.

[01:06:55]>> Okay, sir. Okay, sir.

[01:06:57]>> Not down all these notes very clearly.

[01:06:59]Okay. Bye. This is the one.