Let ABand X be sets Let ABand X be sets a Prove that if the

Let A,B,and X be sets

Let A,B,and X be sets a) Prove that if , then . Prove that if c) Suppose iff b) Prove that , then

a) A is contained in B means any element in A belongs to B

Thus x\\A means all elements in X- elements in A

is contained in All elements in X-elements in B obviously

Hence proved

A is contained in X.

Then x\\A means Elements in X not in A

X\\(x\\A) = elements in X and in A = A

Converse: given that

X\\(x\\A) = elements in X and in A = A

This implies

x/A = elements in X not in A

This implies A is contained in X

c) A is contained in X

Thus X\\A = X-A

X-A contains X-B

This implies that there are elements in A which are also in B

Thus each element inA belongs to B.

A is contained in B.