In Exercises 1–6 assume that A is a subset of some underlying universal set U . 1. Prove the complementation law in Table 1 by showing that A = A . 2. Prove the identity laws in Table 1 by showing...

In Exercises 1–6 assume that
A
is a subset of some underlying universal set
U.

1. Prove the complementation law in Table 1 by showing that
A
=
A.

2. Prove the identity laws in Table 1 by showing that

a)
A
∪∅ =
A.

b)
A
∩
U
=
A.

3. Prove the domination laws in Table 1 by showing that

a)
A
∪U
=
U.

b)
A∩∅ = ∅.

4. Prove the idempotent laws in Table 1 by showing that

a)
A
∪A
=
A.

b)
A
∩
A
=
A.

5. Prove the complement laws in Table 1 by showing that

a)
A
∪A
=
U.

b)
A
∩
A
= ∅.

6. Show that

a)
A−∅ =
A.

b) ∅−A
= ∅.