Prove the idempotent laws in Table 1 by showing that

a) A ∪ A = A.

b) A ∩ A = A.

Solution:

Step1

Given that

The idempotent laws in Table.

Step2

To find

We have to prove the idempotent laws .

Step3

Idempotent law states that connection a add with itself either by logical addition or logical multiplication can lead to a logical add or product that's the equivalent of the add.

Example , B+B=B, BB=B.

a) A ∪ A = A

Here , Right hand side=A

And Left hand side=AA

Now

Left hand side=AA

=

=

=

= A= Right hand side.

Therefore, A ∪ A = A.

Step4

b) A ∩ A = A.

Here , Right hand side=A

And Left hand side=A ∩ A

Now

Left hand side=A ∩ A

=

=

=

= A= Right hand side.

Therefore, A ∩ A = A.