Identify the error or errors in this argument that supposedlyshows that if ∃xP(x)∧∃xQ(x)is true then∃x(P(x)∧Q(x))is true. ∃xP(x)∨∃xQ(x) Premise ∃xP(x) Simplification from (1) P(c) Existential instantiation from (2) ∃xQ(x) Simplification from (1) Q(c) Existential instantiation from (4) P(c)∧Q(c) Conjunction from (3) and (5) ∃x(P(x)∧Q(x)) Existential generalization

where free variable =0

1

Suppose that P(n), Q(n) and R(n) are statements about the integer n. Let S(n) be the statement: “If P(n) is true then Q(n) and R(n) are both true." (a) The contrapositive of S(n) is the statement Olf Q (n) and R(n) are both true then P(n) is false. Olf Q (n) and R(n) are both true then P(n) is true. Olf at least one of Q(n) and R(n) is false then P(n) is false. Olf Q (n) and R(n) are both false then P(n) is false. Olf at least one of Q(n) and R(n) is false then P(n) is true. Olf P(n) is false then at least one of Q(n) and R(n) is false. Olf Q (n) and R(n) are both false then P(n) is true. ONone of the other answers. (b) The statement: "If Q (n) and R(n) are both true then P(n) is true." is OThe converse of S(n). OThe contrapositive of S(n). OThe converse of the contrapositive of S(n). ONone of the other answers.