CSCE 235

Handout 4: Logical Equivalences and Implications

January 14, 2004

Logical Equivalences

1. double negation

2.a.

2.b. commutative laws

2.c.

3.a.

3.b. associative laws

4.a.

4.b. distributive laws

5.a.

5.b. idempotent laws

6.a.

6.b.

6.c.

6.d. identity laws

7.a.

7.b. negation laws

8.a.

8.b.

8.c.

8.d. DeMorgan laws

9. contrapositive

10.a.

10.b. implication

11.a.

11.b.

12.a.

12.b.

13. equivalence

14. exportation law

15. reductio ad absurdum

Logical Implications

16. addition

17. simplification

18. absurdity

19. modus ponens

20. modus tollens

21. disjunctive syllogism

22.

23. transitivity of

24. transitivity of of hypothetical syllogism

25.a.

25.b.

25.c.

26.a.

26.b. constructive dilemmas

27.a.

27.b. destructive dilemmas

Based on (Ross and Wright 1988).