Show that p rightarrow (q rightarrow r) and q rightarrow (p r) are logically equivalent. Define the logical operator downarrow as NOR: p downarrow q is true when both p and q are false, and otherwise it is false. (a) Show that p downarrow p is logically equivalent to p. (b) Show that (p downarrow q) downarrow (p downarrow q) is logically equivalent to p q. Determine whether each of the compound propositions below is satisfiable. (a) (p q r) (p q s) (p r s) ( p q s) (p q s) (b) ( p q r) ( p q s) (p q s) ( p r s) (p q r) (p r s)