Construct a truth table for the given statement.    p ∧ (q ∨ ~p)   ∨ r p q r ~p q ∨ ~p p ∧ (q ∨ ~p)  p ∧ (q ∨ ~p)   ∨ 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

Using one or more truth tables, determine which pairs of the following statements are and are not equivalent. • p q • pq P→→q p¬q

Suppose P, Q and R are statements. Complete the truth table for the statement (P ⇒ R) and (P or (not Q)). P Q R (PR) and (P or (not Q)) true true true true true false true false true true false false false true true false true false false false true false false false ♦ ◆

Use the statements and truth table to determine which statements are equivalent. p: It is a fish. q: It eats algae. pqpqpq ~p~q qp ~q → ~p TT F FL T T T T TF F T F T T F FT T LL F T F LL F T FF T T T T T Τ If it eats algae, then it is a fish. It is a fish, and it eats algae. If it is a fish, then it does not eat algae. It is a fish, or it eats algae. If it is a fish, then it eats algae. If it does not eat algae, then it is a fish. If it eats algae, then it is a fish. If it is not a fish, then it does not eat algae.