WEBVTT 00:00:00.680 --> 00:00:02.740 Let's define ourselves some sets. 00:00:02.740 --> 00:00:08.530 So let's say the set A is composed of the numbers 1. 00:00:08.530 --> 00:00:09.510 3. 00:00:09.510 --> 00:00:13.880 5, 7, and 18. 00:00:13.880 --> 00:00:16.980 Let's say that the set B-- let me 00:00:16.980 --> 00:00:18.640 do this in a different color-- let's 00:00:18.640 --> 00:00:26.010 say that the set B is composed of 1, 7, and 18. 00:00:26.010 --> 00:00:38.522 And let's say that the set C is composed of 18, 7, 1, and 19. 00:00:38.522 --> 00:00:40.730 Now what I want to start thinking about in this video 00:00:40.730 --> 00:00:42.950 is the notion of a subset. 00:00:42.950 --> 00:00:48.752 So the first question is, is B a subset of A? 00:00:48.752 --> 00:00:50.960 And there you might say, well, what does subset mean? 00:00:50.960 --> 00:00:53.590 Well, you're a subset if every member of your set 00:00:53.590 --> 00:00:56.410 is also a member of the other set. 00:00:56.410 --> 00:01:01.976 So we actually can write that B is a subset-- 00:01:01.976 --> 00:01:03.600 and this is a notation right over here, 00:01:03.600 --> 00:01:08.647 this is a subset-- B is a subset of A. B is a subset. 00:01:08.647 --> 00:01:09.730 So let me write that down. 00:01:09.730 --> 00:01:19.260 B is subset of A. Every element in B is a member of A. 00:01:19.260 --> 00:01:21.040 Now we can go even further. 00:01:21.040 --> 00:01:23.950 We can say that B is a strict subset of A, 00:01:23.950 --> 00:01:26.830 because B is a subset of A, but it does not 00:01:26.830 --> 00:01:29.850 equal A, which means that there are things in A that are not 00:01:29.850 --> 00:01:32.680 in B. So we could even go further 00:01:32.680 --> 00:01:34.750 and we could say that B is a strict 00:01:34.750 --> 00:01:37.245 or sometimes said a proper subset of A. 00:01:37.245 --> 00:01:39.690 And the way you do that is, you could almost 00:01:39.690 --> 00:01:42.380 imagine that this is kind of a less than or equal sign, 00:01:42.380 --> 00:01:44.590 and then you kind of cross out this equal part 00:01:44.590 --> 00:01:46.080 of the less than or equal sign. 00:01:46.080 --> 00:01:48.440 So this means a strict subset, which 00:01:48.440 --> 00:01:51.770 means everything that is in B is a member A, 00:01:51.770 --> 00:01:54.060 but everything that's in A is not a member of B. 00:01:54.060 --> 00:01:55.050 So let me write this. 00:01:55.050 --> 00:02:03.920 This is B. B is a strict or proper subset. 00:02:03.920 --> 00:02:09.475 So, for example, we can write that A is a subset of A. 00:02:09.475 --> 00:02:12.350 In fact, every set is a subset of itself, 00:02:12.350 --> 00:02:16.330 because every one of its members is a member of A. 00:02:16.330 --> 00:02:21.480 We cannot write that A is a strict subset of A. 00:02:21.480 --> 00:02:26.310 This right over here is false. 00:02:26.310 --> 00:02:29.250 So let's give ourselves a little bit more practice. 00:02:29.250 --> 00:02:37.082 Can we write that B is a subset of C? 00:02:40.639 --> 00:02:41.305 Well, let's see. 00:02:41.305 --> 00:02:45.320 C contains a 1, it contains a 7, it contains an 18. 00:02:45.320 --> 00:02:47.940 So every member of B is indeed a member 00:02:47.940 --> 00:02:51.640 C. So this right over here is true. 00:02:51.640 --> 00:02:54.380 Now, can we write that C is a subset? 00:02:54.380 --> 00:03:00.665 Can we write that C is a subset of A? 00:03:00.665 --> 00:03:04.490 Can we write C is a subset of A? 00:03:04.490 --> 00:03:05.700 Let's see. 00:03:05.700 --> 00:03:09.940 Every element of C needs to be in A. So A has an 18, 00:03:09.940 --> 00:03:11.940 it has a 7, it has a 1. 00:03:11.940 --> 00:03:13.910 But it does not have a 19. 00:03:13.910 --> 00:03:20.196 So once again, this right over here is false. 00:03:20.196 --> 00:03:21.570 Now we could have also added-- we 00:03:21.570 --> 00:03:23.710 could write B is a subset of C. Or we could even 00:03:23.710 --> 00:03:28.260 write that B is a strict subset of C. 00:03:28.260 --> 00:03:32.145 Now, we could also reverse the way we write this. 00:03:32.145 --> 00:03:34.270 And then we're really just talking about supersets. 00:03:34.270 --> 00:03:36.110 So we could reverse this notation, 00:03:36.110 --> 00:03:43.015 and we could say that A is a superset of B, 00:03:43.015 --> 00:03:45.640 and this is just another way of saying that B is a subset of A. 00:03:45.640 --> 00:03:49.400 But the way you could think about this is, 00:03:49.400 --> 00:03:53.570 A contains every element that is in B. 00:03:53.570 --> 00:03:55.100 And it might contain more. 00:03:55.100 --> 00:03:56.970 It might contain exactly every element. 00:03:56.970 --> 00:03:59.452 So you can kind of view this as you kind of 00:03:59.452 --> 00:04:00.660 have the equals symbol there. 00:04:00.660 --> 00:04:02.870 If you were to view this as greater than or equal. 00:04:02.870 --> 00:04:04.837 They're note quite exactly the same thing. 00:04:04.837 --> 00:04:06.420 But we know already that we could also 00:04:06.420 --> 00:04:13.320 write that A is a strict superset of B, which 00:04:13.320 --> 00:04:17.140 means that A contains everything B has and then some. 00:04:17.140 --> 00:04:21.690 A is not equivalent to B. So hopefully this familiarizes you 00:04:21.690 --> 00:04:31.130 with the notions of subsets and supersets and strict subsets.