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Subsets

Recall that a set is a collection of elements.

A set A is a subset of a set B if every element in A is also in B .

For example, if A = { 1 , 3 , 5 } and B = { 1 , 2 , 3 , 4 , 5 } , then A is a subset of B , and we write

A B

The line under the sideways means that A may also be equal to B (that is, they may be identical sets). If we want to say that A is a proper subset of B (that means: it's a subset, but there is at least one element in B that is not in A ) then we can remove the line:

A B

To write that a set is not a subset of another set, just put a slash through the sideways :

B A

 

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