Prove De Morgan's law by showing that each side is a subset of the other side by considering x ∈ A⎯⎯⎯ A ¯ ∩ B⎯⎯⎯ B ¯ .

Solution :

We have to prove that   (De-Morgan's law)

Let   then and

and so and .

Thus, and so

Hence,   .........(1)

Now we will show that

Let ⇒

Thus x is present neither in the set A nor in the set B, so by definition of the union of the sets, by definition of the complement.

and  

Therefore, and we have  .............(2)

From (1) and (2),

Hence proved.

i think c. but don't trust it.

step-by-step explanation: