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

Question

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 = ∅.

David · Accepted Answer

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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...