1 00:00:00,680 --> 00:00:02,740 Let's define ourselves some sets. 2 00:00:02,740 --> 00:00:08,530 So let's say the set A is composed of the numbers 1. 3 00:00:08,530 --> 00:00:09,510 3. 4 00:00:09,510 --> 00:00:13,880 5, 7, and 18. 5 00:00:13,880 --> 00:00:16,980 Let's say that the set B-- let me 6 00:00:16,980 --> 00:00:18,640 do this in a different color-- let's 7 00:00:18,640 --> 00:00:26,010 say that the set B is composed of 1, 7, and 18. 8 00:00:26,010 --> 00:00:38,522 And let's say that the set C is composed of 18, 7, 1, and 19. 9 00:00:38,522 --> 00:00:40,730 Now what I want to start thinking about in this video 10 00:00:40,730 --> 00:00:42,950 is the notion of a subset. 11 00:00:42,950 --> 00:00:48,752 So the first question is, is B a subset of A? 12 00:00:48,752 --> 00:00:50,960 And there you might say, well, what does subset mean? 13 00:00:50,960 --> 00:00:53,590 Well, you're a subset if every member of your set 14 00:00:53,590 --> 00:00:56,410 is also a member of the other set. 15 00:00:56,410 --> 00:01:01,976 So we actually can write that B is a subset-- 16 00:01:01,976 --> 00:01:03,600 and this is a notation right over here, 17 00:01:03,600 --> 00:01:08,647 this is a subset-- B is a subset of A. B is a subset. 18 00:01:08,647 --> 00:01:09,730 So let me write that down. 19 00:01:09,730 --> 00:01:19,260 B is subset of A. Every element in B is a member of A. 20 00:01:19,260 --> 00:01:21,040 Now we can go even further. 21 00:01:21,040 --> 00:01:23,950 We can say that B is a strict subset of A, 22 00:01:23,950 --> 00:01:26,830 because B is a subset of A, but it does not 23 00:01:26,830 --> 00:01:29,850 equal A, which means that there are things in A that are not 24 00:01:29,850 --> 00:01:32,680 in B. So we could even go further 25 00:01:32,680 --> 00:01:34,750 and we could say that B is a strict 26 00:01:34,750 --> 00:01:37,245 or sometimes said a proper subset of A. 27 00:01:37,245 --> 00:01:39,690 And the way you do that is, you could almost 28 00:01:39,690 --> 00:01:42,380 imagine that this is kind of a less than or equal sign, 29 00:01:42,380 --> 00:01:44,590 and then you kind of cross out this equal part 30 00:01:44,590 --> 00:01:46,080 of the less than or equal sign. 31 00:01:46,080 --> 00:01:48,440 So this means a strict subset, which 32 00:01:48,440 --> 00:01:51,770 means everything that is in B is a member A, 33 00:01:51,770 --> 00:01:54,060 but everything that's in A is not a member of B. 34 00:01:54,060 --> 00:01:55,050 So let me write this. 35 00:01:55,050 --> 00:02:03,920 This is B. B is a strict or proper subset. 36 00:02:03,920 --> 00:02:09,475 So, for example, we can write that A is a subset of A. 37 00:02:09,475 --> 00:02:12,350 In fact, every set is a subset of itself, 38 00:02:12,350 --> 00:02:16,330 because every one of its members is a member of A. 39 00:02:16,330 --> 00:02:21,480 We cannot write that A is a strict subset of A. 40 00:02:21,480 --> 00:02:26,310 This right over here is false. 41 00:02:26,310 --> 00:02:29,250 So let's give ourselves a little bit more practice. 42 00:02:29,250 --> 00:02:37,082 Can we write that B is a subset of C? 43 00:02:40,639 --> 00:02:41,305 Well, let's see. 44 00:02:41,305 --> 00:02:45,320 C contains a 1, it contains a 7, it contains an 18. 45 00:02:45,320 --> 00:02:47,940 So every member of B is indeed a member 46 00:02:47,940 --> 00:02:51,640 C. So this right over here is true. 47 00:02:51,640 --> 00:02:54,380 Now, can we write that C is a subset? 48 00:02:54,380 --> 00:03:00,665 Can we write that C is a subset of A? 49 00:03:00,665 --> 00:03:04,490 Can we write C is a subset of A? 50 00:03:04,490 --> 00:03:05,700 Let's see. 51 00:03:05,700 --> 00:03:09,940 Every element of C needs to be in A. So A has an 18, 52 00:03:09,940 --> 00:03:11,940 it has a 7, it has a 1. 53 00:03:11,940 --> 00:03:13,910 But it does not have a 19. 54 00:03:13,910 --> 00:03:20,196 So once again, this right over here is false. 55 00:03:20,196 --> 00:03:21,570 Now we could have also added-- we 56 00:03:21,570 --> 00:03:23,710 could write B is a subset of C. Or we could even 57 00:03:23,710 --> 00:03:28,260 write that B is a strict subset of C. 58 00:03:28,260 --> 00:03:32,145 Now, we could also reverse the way we write this. 59 00:03:32,145 --> 00:03:34,270 And then we're really just talking about supersets. 60 00:03:34,270 --> 00:03:36,110 So we could reverse this notation, 61 00:03:36,110 --> 00:03:43,015 and we could say that A is a superset of B, 62 00:03:43,015 --> 00:03:45,640 and this is just another way of saying that B is a subset of A. 63 00:03:45,640 --> 00:03:49,400 But the way you could think about this is, 64 00:03:49,400 --> 00:03:53,570 A contains every element that is in B. 65 00:03:53,570 --> 00:03:55,100 And it might contain more. 66 00:03:55,100 --> 00:03:56,970 It might contain exactly every element. 67 00:03:56,970 --> 00:03:59,452 So you can kind of view this as you kind of 68 00:03:59,452 --> 00:04:00,660 have the equals symbol there. 69 00:04:00,660 --> 00:04:02,870 If you were to view this as greater than or equal. 70 00:04:02,870 --> 00:04:04,837 They're note quite exactly the same thing. 71 00:04:04,837 --> 00:04:06,420 But we know already that we could also 72 00:04:06,420 --> 00:04:13,320 write that A is a strict superset of B, which 73 00:04:13,320 --> 00:04:17,140 means that A contains everything B has and then some. 74 00:04:17,140 --> 00:04:21,690 A is not equivalent to B. So hopefully this familiarizes you 75 00:04:21,690 --> 00:04:31,130 with the notions of subsets and supersets and strict subsets.