follow from previously given laws, in the sense that it is possible to transform p + pq into p and transform p(p + q) into p using only laws 1 through 17.

1. Reflexivity of equivalence : p p.

2. Commutative law for equivalence : (p q) (q p).

3. Transitive law for equivalence : ((p q) AND (q r)) (p r). 4. Equivalence of the negations : (p q) (p q).

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.

14. The distributive law for OR over AND : (p + qr) ((p + q)(p + r)). 15. 1istheannihilatorforOR:(1ORp)1.

16. Idempotence of AND : pp p. 17. Idempotenceof OR:p+pp.