Show using a direct proof and logical operators the following set equality.A−BC= A∩B

Show using a direct proof and logical operators the following set equality.A−B^C= A∩B

Expert Solution

Let us consider, for every x we have, x A B

So, x does not belong in B^C as it is in B and x A

So, for every value of x, we have x A - B^C

So, from this we can say that, A B will be subset of A - B^C

Let us consider, for every y we have, y A - B^C

So, y does not belong in B^C as it is in B and y A

Also, y B.

So, for every y A B

So, from this we can say that, A - B^C will be subset of A B

So, we can say that A B = A - B^C (proved)

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venereology answered 2 years ago

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