I'll do a), c), and e). To construct a truth table: Begin every truth table that has two letters like this p | q | ------- T | T | T | F | F | T | F | F | Begin every truth table that has three letters like this: p | q | r | ----------- T | T | T | T } T | F | T | F | T | T | F | F | F | T | T | F | T | F | F | F | T | F | F | F | Rule for "not": 1. If "not" precedes T, it becomes F 2. If "not" precedes F, it becomes T Rule for "or: "or" is T except when there are F's on both sides of "or". Then it's F. Rule for "and": "and" is F except when there is T's on both sides of "and". Then it's T. a) not (p and q) p | q | p and q | not(p and q) | -------------------------------- T | T | T | F | T | F | F | T | F | T | F | T | F | F | F | T | c) (not P) or (not q) p | q | (not p) | (not q) | (not P) or (not q) | ------------------------------------------------ T | T | F | F | F | T | F | F | T | T | F | T | T | F | T | F | F | T T | T | e) (P or R) and (Q or R) P | Q | R | (P or R) | (Q or R) | (P or R) and (Q or R) | --------------------------------------------------------- T | T | T | T | T | T | T } T | F | T | T | T | T | F | T | T | T | T | T | F | F | T | F | F | F | T | T | T | T | T | F | T | F | F | T | F | F | F | T | T | T | T | F | F | F | F | F | F | Edwin