HOW TO SOLVE SET THEORY QUESTIONS

[00:00:00]We are given seting to look at tonight.

[00:00:02]So the set A, B and C as subsets of the universal set U equals 1 2 3 to 14. And we are given the subset A as a set of even numbers and the subset B as a factors of 24 and the and the subset C 3 6 9 12. These are the three that we are given to uh tonight. Then we are given a question. Question one to list the elements of A and B. And the second one here is that we should find the intercept of A and C. The intercept of A and C. So we are now going to look at what we have in each of them. This is universal set. All right. You just said I have all the numbers from 1 to 14 and we have even numbers. We have even numbers here. So we are going to pick the even numbers in this set to make set a. So this is how we are going to follow through.

[00:01:23]This is how we are going to follow through. So first a set a is the set of even numbers in the universal set. So what are the even numbers here? We are going to start from two. Okay. All the numbers that two can divide are even numbers. So we have two then we have four we have six then we have 8. We have 10, we have 12, and we have 14.

[00:01:59]These are all the even number sets.

[00:02:02]Okay, these are all the even number sets that are here. So, and that is the subset of A, the sets of even numbers.

[00:02:12]Then for B, for B we have factors of 24. So all these numbers, which of them can divide 24? All right. So we going to put it inside this set or subset B which is which are the factors of 24 includes one. One can divide 24. All the numbers that can divide 24 one. Okay. 1 can divide 24. Two can divide 24. 3 can divide 24.

[00:02:50]3 can divide 24. Then 4 can divide 24.

[00:02:55]Okay. 6 can divide 24.

[00:03:00]7 cannot divide 24. But 8 can go into 24.

[00:03:05]9 cannot divide 24. 10 cannot divide 24.

[00:03:10]11 cannot divide 24 but 12 can divide 24.

[00:03:15][snorts] All right. So these are the factors of of 24 in this set. Okay. In universal set. So this is what we have done and that is the factors look at the set of the factors of 24 is the subset B. Right? Then we know our C our C remains what we have here. All right. So C equals the subset of three then six then we have 9 and we have 12 here.

[00:03:52]So that's all. Now we are given the question to answer list the elements of A and B. We are going to list the elements of A and B.

[00:04:04]Then find A inter B. So before I start, thank you very much and welcome to AS Science TV. Okay, AS Science TV is a channel where we are much more committed in live streaming mathematical solutions because we know this is how students find mathematics easier to understand where it is done live. All right, that's a science TV for you. We believe that um making mathematics live is going to be helpful to the students. So that's why we are doing it this way. We want student to enjoy mathematics in as much as they are learning. So as we are learning together, we are still enjoying it. If you are joining me for the first time and you have not subscribed, please do to smash the subscribe button. Okay. Now without much ado, let's continue where we stop right now. So here we are able to make out for the three subsets A, B, C, which is what we are given here. So question A is simple. So what is question A? Question A is what we have answered here. List the elements of A and B. So we have listed the elements of A and B. So that is question A. So we don't need to rewrite it again. We have already answered the question. Okay. A and B set of even numbers. These are the sets of even numbers. Then set B is a set of the factors of 24.

[00:05:36]Then C, we don't need to bother ourel with C. Just write C here if you need.

[00:05:42]Okay, but let's just put it the way we have done it. Then for B, we are told to find A intercept C. This symbol is called intercept. Intercept means what they have in common. So what does A and C have in common? Right? We are going to find out what A and C have in common. So that is B A inter C.

[00:06:12]So what is the set of A inter C?

[00:06:19]So what does A and C have in common?

[00:06:23]Let's check. This is A and this is C. We have two here. There's no two here. We have four. There's no four. We have six and there is six here. So six is one of the numbers. You can see here we have six in A and C. All right. Then we have eight here. No eight here. 10 here. No 10 here. 12. We have 12 here.

[00:06:47]We have 12 here. All right. So this is this is the set of A inter C. All right.

[00:06:56]So this topic is quite straightforward and very easy to comprehend. Okay. So this is set theory and that's what we are doing today. Thank you very much for joining me. This is the second time we are having our class today and we do hope you are finding value in my video and if you are joining me for the first time and you have not subscribed please do well to smash subscribe button. AZ Science TV is committed to making mathematics very friendly and easier.

[00:07:21]Some student always see math very scary but in AZ Science TV we tell you that mathematics is the subject I can enjoy better than so many other subjects.

[00:07:32]Mathematics is like a game of numbers just like we are doing it right now.

[00:07:36]This is mathematics is not harder than this. All right. So please let's proceed. Let me repeat what we have we have said so far. Um here we are told that the sets of A, B and C are subsets of the inversal set U. Okay having 1 2 3 to 14 as the elements. So these are the subsets A, B and C. So the subset of A is the set of even numbers between 1 and or from 1 to 14. Okay. While the subset of B are the factors of 24 in that universal set, right? This set. Then C are these numbers listed here. So the set of 3 6 9 and 12. And question A, we are told to list the elements of A and B. So you can see that we have listed the elements of A and the elements of B.

[00:08:39]All right. Then in in B we are told to find A inter C. So we are going to do it gradually. A the subset A is the set of even numbers. So we are going to get the even numbers from 1 to 14. Even numbers are numbers that are divisible by two as in two can divide them. Any number that two can divide and the number is here starting from one. We check the numbers that two can divide here. Okay. And that's what we are going to be writing down here. So two cannot divide one. We strike that away. Then two can divide two 4 6 8 10 12 and 14. 14 is the last number here. And two can also divide 14.

[00:09:27]So this means that the set of the even numbers from 2 to 14. Okay. Is a subset a. Then for the second one which is B subset B is the set that represent the factors of 24. All the factors of 24 starting from 1 to 14.

[00:09:49]So which of them are the factors of 24?

[00:09:53]We are going to start one is a factor of 24. A factor of 24 means numbers that can divide 24.

[00:10:04]Okay. If they cannot divide 24, please don't pick them. All right? So, we only pick the ones that can divide 24 to make the subset of B. Okay? To make the subset B. All right? So, one can divide 24. And there is one here. So, we'll pick it. Two can divide 24. Three can divide 24. Four can divide 24.

[00:10:25]6 can divide 24. Not five. Okay. 8 can divide 24. Not seven.

[00:10:33]9 cannot divide 24. 10 cannot divide 24.

[00:10:37]Okay. 11 cannot divide 24. But 12 can divide 24. 13 and 14 cannot divide what?

[00:10:43]24. So these are the elements of the set.

[00:10:49]Okay? Because all these elements here all the numbers here can divide 24. So they are all factors of 24.

[00:10:58]So we have been able to answer question A. The first question here we are able to answer these questions. All right. So these questions consist of elements A and B which are questions that can elements that can divide 24. Then the second one is that we should find A inter C. A inter C. A inter C means uh A and C. What do they have in common? All right. That's [snorts] what they have.

[00:11:32]What do they have in common? Now we are going to check A and check C. So what do what do they have in common? All right.

[00:11:42]So here we see that A we have two here but we don't have two here. A we have four but there is no four here. Then there is six here and we have six here.

[00:11:56]So six is common between A and C. So we write six here because six is common.

[00:12:03]Then there is no eight in C. There is no 10 here. But there is 12. You can see that 12 is common here between A and C.

[00:12:14]So we write six and 12. So this these are the two numbers that make up the sets of the intercept of A and C. I hope it is understood. Thank you very much for joining me on AZ Science TV. I do appreciate the fact that you are always with us. Thank you. I appreciate you for coming. I hope your day was wonderful.

[00:12:37]If you are joining me for the first time and you have not subscribed, please just smack the subscribe button so that you can always be a part of yeah of this channel. Thank you for being here. U we are going to quickly look at the next question for tonight. So let's please be attentive. Thank you very much for being here. [snorts] >> [screaming] >> Fight.

[00:14:29]This is a very simple question as well.

[00:14:32]Okay, that this with set. All right, this is another question. Here we have X is a set of A B C D E F and Y is a set of A C D. So here we are told to find the set of X inter Y. Sorry is X intercept Y. H X intercept Y. Why? Here it is X intercept Y complement. This is complement. All right. So how do we handle this? This is how we are going to do it. It's quite easy. Okay. It means we are going to list the elements of X inter Y. All right. How do we list these elements?

[00:15:27]Look at it. X intercept Y equals.

[00:15:35]So we are going to list what do they have in common. What does X and Y or what do X and Y have in common?

[00:15:44]A is common to X and Y. A is common. So we are going to write A. B is common to X and Y. So we going to write B.

[00:15:58]C is common to X and Y. So we are going to write C.

[00:16:03]and D is also common to X and Y. So we are going to write D. Then we close the bracket like this. This is called set bracket. Not the ordinary usual bracket.

[00:16:14]But this is a separate type a specific or pecular types of of bracket. All right. It's called set bracket. Now we have been able to list the elements of the set that denotes X intercept Y. So you notice that these elements are common to both X and Y. All right? So you're going to see it here. A C D A C sorry. So we have A C D A C D. Okay? Because there is no B here.

[00:16:49]There's no B just AC. This is the set of X intercept Y. Then the second one here is is x intercept y but this time it is the complement.

[00:17:08]What does it imply? The word complement means the absentees of this set. What elements are not are absent here but they are present in the original universal set or universal set.

[00:17:25]Okay, then we all know that there is no universal set here. These are the two of them are me subsets. Okay, so let's say uh u we can bring in universal sets to be a b c d e f and g. Okay. So if this is the inversal set for instance okay and then we are looking for X inter Y complement now we can look at it X interct Y give us A C and B so we are going to subtract this set from the inversal set and write what is left a we are going to cancel A then there's no B to cancel B so B is a member of the complement of this set. Then C we cancel C. D we cancel D.

[00:18:27]So we are left with E, F, G. So we are going to write E, F and G. So this is the the set H. This is the set of the complement of X intercept Y. All right? You'll notice that when we combine these two, we'll get the universal set. A B C D E F G A B C D E F G So these are the elements and I hope this answers the question and clarifies every hidden areas. Thank you for joining me. A Science TV is very grateful for having you. Your presence here is actually promoting this channel.

[00:19:13]I appreciate you for your views, your comments, your appreciation, everything else. Okay, I see your comments and your and your emojis and the rest. They are very wonderful. I appreciate you. I say thank you very much for always joining me. A Science TV cannot exist without you. So, your presence here is the reason we are here. If you are not there, there no need for me to be here.

[00:19:34]Please, if you are joining me for the first time, do well to encourage us by smashing the subscribe button if you have not subscribed. Okay, please. I do hope that you are getting values from this video. Thank you for always being here. I appreciate you. And for the for those that are just viewing us for the first time, this is AZ Science TV. It's a channel where we are committed to stream live to to solving mathematical problems or questions live. Okay, we stream mathematics live just for you to see how it works live. Okay, not just with videos but with live live streams.

[00:20:08]That's what we are very much committed to doing. So we appreciate you for joining me. Uh please do well to smash the subscribe button. Every Saturday from 9 to 10:30 we usually hold our mathematical weekend. Then every morning we hold another very powerful class.

[00:20:25]Every morning known as good morning mathematics that is the show every morning. Please do to join us between 7:30 and quarter and between 6:30 and quarter 7. So we appreciate you for coming. Thank you very much for joining.

[00:20:41]Let me review what I have said so far for those that are just um hooking up to ush just now. Okay. Here we are given universal set A B C D E F G and we're given X and Y as the subsets of the universal set. Then here the the the subsets are X and and X set X is a subset of or is a set of A B C D E F and set Y okay is a set of elements A C D.

[00:21:19]So what it implies is that these are the contents or the elements of set X while these are the elements of set Y of set Y. This is for X while this is for Y.

[00:21:30]Then we are told to find X intercept Y which means what do what do they have in common? What does X and Y have in common? That is X intercept Y. Then that is what we have done here. Look at it.

[00:21:45]We are looking at what X and Y have in common. A A is common so we take one A just take one please it should not be repeated okay if we are repeating it then it's no longer set H so we are not going to repeat it we take only one here which is A here then C and C we take C then D and D we take D so this these are the elements of the set of the inter of X and Y all right and the second one is X intercept Y complement. So what will be the intercept? What will be the intercept of this? It's going to be B E FG. How do I get it? This is X intercept Y. Use A C D to divide the elements of the inverse set. Then write what is remaining here. Okay. A cancels A, C cancels C and D cancels D. we are left with B E F G and that is B E F G. So that is how to solve this particular uh problem. This has no serious uh it's like a game like playing games. All right, that's mathematics for you. So thank you for being here. Please don't forget to subscribe. I'm waiting for a subscription. Okay, for those who have subscribed, thank you very much for subscribing. I know you actually meant well for the channel. That is why you smash subscribe button. For those that are still watching have not subscribed, please just do well. Then my subscribers that are always coming to watch this uh your channel in fact I cannot appreciate you more than enough. You are the reason behind the the rapid growth of the channel. You you are coming back as a subscriber to watch it. So that this is what makes YouTube to promote the video more and more to more people. So if somebody subscribes today, tomorrow it's because of the subscribers that are returning. A lot of them are coming back to watch. So we appreciate you for that.

[00:23:43]Thank you very much for h for coming to watch and I appreciate you for that. Now let's quickly take the next question.

[00:24:36]Keep on good.

[00:25:21]Yes.

[00:25:30]All right.

[00:25:39]So thank you. This is another question.

[00:25:42]This is the third question. Okay. In the in our um series tonight. Now we are given P as the set of numbers from 1 to 8 and we are given Q as a subset and R as a subset. Although they are all subsets because there's no universal sets. So we don't have universal set here. They are all subset. There's no universal set. So there's no need for subsets. They are all set on their own. All right. Then we are given P intercept Q union arrow. So we are going to find P intercept Q. Then we give it a union with arrow. So P intercept Q means what they have in common.

[00:26:31]So we have P intercept Q union R.

[00:26:41]So it's something like this. So what is P intercept Q? Very important. P intercept Q= to what does P and Q have in common? That is the first thing we are going to do. So this is P and Q.

[00:26:58]What do they have in common? This is P and Q. So let's check. They have one and one in common. So we write we write one.

[00:27:09]Then two. Do they have two and two in common? No. What about three? No. Then four. They have four in common. P and Q have four in common. So write four. Then nothing else is left except seven. So let's check if seven is common. You can see that seven is in Q and it's in P. So they have it in common. We write seven here. Okay. We have gotten P inter Q.

[00:27:37]And we already know R as 2 48.

[00:27:41]So we want to combine it with this now.

[00:27:44]Right? We know our arrow. Where is our arrow? Arrow is a set of 2 4 8. Arrow is the set of 2 48. Now we want to combine this one. Okay. What we call union. Sorry for this. Okay.

[00:28:03]This is union. H. We want to combine it.

[00:28:07]We want to put it together. Union means to to bring together. All right. to add all the elements together as in to combine them together. So it means that we have P intercept Q brackets then union r okay union arrow so that is going to be we are going to add these two elements combine together we're not using plus just to combine them together without repeating any elements. Remember we have four and four here. We are going to take only one of the four. We won't take the two. Let's start from the list so that we can be well organized. The list here is one. So we are going to write one here. Then the second one is two. So we are going to write two.

[00:28:58]There's no three. So we go to four.

[00:29:01]Remember four is two. Okay. Four occurs twice. Please take one not both of them.

[00:29:08]Then we have seven. So we write seven here. Then we have eight here and this is eight. So this is the solution to this particular question. All right.

[00:29:21]Which means we have to find the intersection of P and Q which is what P and Q have in common. Then we go ahead and unite it by combining the elements of P intercept Q with the elements in arrow. And when doing this we do not repeat the elements. Okay. If two if we have two elements repeating themselves we take just one like four and four here we are not going to take the four and write four two times. We write four just once. So that is how to do it. Thank you very much for being here. You can see that the the solution is fast, straightforward,