Prove the complement laws in Table 1 by showing that

a)

b)Solution:

Step1

Given that

The complement laws .

Step2

To find

We have to prove the complement laws.

Step3

Complement laws :- The supplement of a set B refers to components not in B.

a)

Here , Right hand side=

And Left hand side=

Now

Left hand side=

=

=

=

=

= U

= Right hand side

Therefore,.

Step4

b)

Here , Right hand side=Ø

And Left hand side=

Now

Left hand side=

=

=

= Ø

= Right hand side.

Therefore, =Ø