Problem 20

Use laws given in this section to transform the first of each pair of expressions into the second. To save effort, you may omit steps that use laws 5 through 13, which are analogous to arithmetic. For example, commutative and associativity of AND and OR may be assumed.

a) Transform pq+rs into (p+r)(p+s)(q+r)(q+s).

b) Transform pq + pqr into p(q + r).

5. The commutative law for AND : pq qp.

6. The associative law for AND : p(qr) (pq)r.

7. ThecommutativelawforOR:(p+q)(q+p).

8. TheassociativelawforOR:(p+(q+r))((p+q)+r).

9. The distributive law of AND over OR : p(q + r) (pq + pr).

10. 1(TRUE) is the identity for AND : (p AND 1) p.

11. 0(FALSE) is the identity for OR : p OR 0 p.

12. 0 is the annihilator for AND : (p AND 0) 0.

13. Elimination of double negations : (NOT NOT p) p.