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# Subset, strict subset, and superset

## Video transcript

let's define ourselves some sets so let's say the set a is composed of the numbers 1 3 5 7 and 18 let's say that the set B the set let me do this in a different color let's say that the set B is composed of 1 7 and 18 and let's say that the set C is composed of 18 7 1 and 19 now what I want to start thinking about in this video is the notion of a subset so the first question is is B a subset of a and there you might say what would a subset mean well you're a subset if every member of your set is also a member of the other set so we actually can write that B B is a subset and this is the notation right over here this is a subset B is a subset of a B is a subset so let me write that down B is subset subset of a every element in B is a member of a now we can go even further we can say that B is a strict subset of a because b is a subset of a but it does not equal a which means that there are things in a that are not in B so we could even go further and we could say that B is a strict or sometimes that a proper subset of a and the way you do that is you're essentially you can almost imagine that this is kind of a less than or equal sign and then you kind of cross out the equal part of the less than or equal sign so this means a strict subset which means be everything that is in B is a member of a but everything that's in a is not a member of B so let me write this this is B B is a strict strict or proper proper subset so for example we can write that a is a subset of a in fact every set is a subset of itself because every of its members is a member of a we cannot write we cannot write that a is a strict subset of a this right over here this right over here is false so let's give us give ourselves a little bit more practice can we write that B B is a subset subset of C B is a subset of C well let's see C contains one it contains a seven it contains an 18 so every member of B is indeed a member of C so this right over here is true now can we write that C is a subset can we write that C is a subset subset of a can we write C is a subset of a let's see a every male element of C needs to be an A so a has an 18 it has a 7 it has one but it does not have a 19 so once again once again this right over here is false now we could have also added we could write B as a subset of C or we could even write that B is a strict strict subset of C now the we could also reverse the way we write this and then we're really just talking about super sets so we could reverse this notation and we could say that a is a superset a superset of B which and this is just another way of saying that B is a subset of a but the way you could think about it the way you could think about this is a contains every element that is in B and it might contain more it might contain exactly every element because this you can kind of view this as you know you kind of have the equal symbol there if you were to view this as greater than or equal there not a quite exactly the same thing but we know already that we could also write that a is a strict superset is a strict superset of B which means that a contains everything B has and then some a is not equivalent to B so hopefully this familiarizes you with the notions of subsets and supersets subsets and supersets is subsets and supersets and strict subsets