Question 1 Let P(x) bethestatement "the word x contains the letter a" What are the truthvalues of the following? a) P(orange) b) P(lemon) c) P(true) d) P(false) [4 marks) Question 2 State the value of x after the statement if P(x) then x:=1 is executed, where P(x) is the statement "x > 1." Given that thevalue of x when thisstatement is reachedis [3 marks] a) x=0 b)x=1 C) x=2 Question 3 Let P(x) be the statement "x spends more than five hours every weekday in class," where the domain for x consists of all students. Express each of these quantifications in English. [4 marks] a) 3xP(x) b) VxP(x) c) 3x-P(x) d) Vx-P(x) Question 4 Let Q(x) be the statement "x+1>2x". If the domain consists of all integers, what are these truth values? a) Q(1) b) 3xQ(x) c) WxQ(x) d) 3x-Q(x) e) Wx-Q(x) [5 marks) Questions Determine the truth value of each of these statements if the domain of each variable consists of all real numbers. [4 marks) a)3x(x2 =2) bax[x? =-1) c) Vx (x +221) d) vx (x2 =x) Question 6 Find a counterexample, if possible, to these universally quantified statements, where the domain for all variables consists of allintegers. (4 marks) a) vx(x+ 2x) b}\x{x>Ovx