CHEM 109C Final: CHEM 109CUCSB109C Gainer Summer 14 Final
Document Summary
February 8, 2007: (8 points) use a truth table (or other methods) to prove the logical equivalence (p q) (q p ) (q p ). P q p q q p (p q) (q p ) Since the truth values of (p q) (q p ) and q p are the same for all possible truth values of p and q, these two sentential forms are logically equivalent. The logical equivalence could also be proved symbolically, as follows: (p q) (q p ) (p q) (q p ) ( p q) ( q p ) (p q) q p. (p q p ) ( q q p ) (p q) (p q) Q p: (12 points) the symmetric di erence of two sets a and b is de ned as. A b = a b a b. (a) (8 pts) draw 3 separate venn diagrams for the sets (i) a b; (ii) (a b) c; and (iii) (a b) c.
