proof SolutionTo prove A B A B Let us assume that element

proof

Solution

To prove : (A)\' (B)\' = (A B)\'

Let us assume that element x (A B)\'

By definition of compliment,

If x (A B)\' then x A B

By definition of ,

(x A B)\'

By definition of Union operator,

(x A x B)\'

which implies,

(x A)\' (x B)\'

or, (x A) (x B)

By definition of compliment,

(x A\') (x B\')

By definition of intersection operator,

x A\' B\'

Thus, every element x which belongs to (A B)\' , it also belongs to A\' B\' and vice-versa.

Therefore, (A)\' (B)\' = (A B)\'

Hence, proved.