1) [4 marks] Let P(x) denote the statement that x > 4 (where x is an integer). What is the truth value of 2) [4 marks] Let B(x, y, z) denote the statement that y is between x and z. What is the truth value of B(1, 2, 3) and B( 3, 1, 2)? 3) 8 marks] Translate these statements into English, where C(x) is "x is a comedian" and F(x) is x is funny" and the domain consists of all people a) Vx(F(x)-C(x) b) Vx(C(x) A F(x)) c) 3x(F(x) C(x)) d) 3x(C(x) A Fx) 4) [8 marks] Suppose that the domain of the propositional function P(x) consists of the integers 1, 2, 3, and 4. Write out each of these propositions using disjunctions, conjunctions, and negations. b) VxP(x) 5) [5 marks] Show that 3xP(x) A3xQx) and 3x(P(x) AQ(x)) are not logically equivalent. Justify your 6) [5 marks] Determine whether Vx(P(x) ? Q(x)) and VP(x) ? hQ(x) are logically equivalent. 7) [8 marks] Let U be (2, -4, 7, -9; for both x and y. Define P(x.y): 3x -2y>1. What is the truth value answer Justify your answer of the following? a) Vx Vy P(x, y) c) 3x Vy P(x, y) d) 3x 3y P(x, y) 8) 8 marks] In each of the following statements use De Morgan's Laws to distribute negations inward (that is, all negations in the resulting equivalent expression should appear before a predicate): a) -3yVxP(xy)