Prove that the union of ~(A and B) is equal to the intersection of ~A and ~B

Prove that the union of ~(A and B) is equal to the intersection of ~A and ~B

This is the first of De Morgan's Laws.

We use the "~" to represent "not".

So first we assume there is an object x that is a member of the union of ~(A and B)
which is true, if and only if(iff) x is not a member of A and B
which is true if x isn't in A and isn't in B
which is the same as x being in ~A and ~B
which is the same as x being in the intersection of ~A and ~B.


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Prove that the intersection of A and B is a subset of A

Prove that the intersection of A and B is a subset of A


Suppose there is a x which is in the intersection of A and B. Therefore that x is also in A, and so the intersection of A and B is a subset of A. ~~~~