Problem 1.20 point (a)Consider the proposition: R=“ For all x∈S,P(x) implies Q(x) For each statement below: · If r implies that statement, then circle→. If R is implied by that statement, then circle Thus, you might circle zero, one or two arrows next to each statement. Circle only implications that hold for all sets S and all predicates P and Q) For all c E s, Q(ar) implies P(a) For all x E S, - Q()implies P(a) or all T E S, P(r)and Q(a) There does not exist an E S such that not(P(ar) implies Q(a)) flQuiz 1 2 Problem 1. [20 points] (a) Consider the proposition: R = “For all x ∈ S, P(x) implies Q(x).” For each statement below: • If R implies that statement, then circle ⇒. • If R is implied by that statement, then circle ⇐. Thus, you might circle zero, one, or two arrows next to each statement. (Circle only implications that hold for all sets S and all predicates P and Q.) ⇒ ⇐ For all x ∈ S, Q(x) implies P(x). ⇒ ⇐ For all x ∈ S, ¬Q(x) implies ¬P(x). ⇒ ⇐ For all x ∈ S, P(x) and Q(x). ⇒ ⇐ There does not exist an x ∈ S such that not (P(x) implies Q(x)). ⇒ ⇐ Pigs fly