Question 1 (4 points) Match the statements that are logically equivalent. (PVQ) - R 1 . ( ( PAQ ) 1, then x > 0. 3. There exists a real number x such that ac2 1, then x>0. 5. For all real numbers x, if 202 0, then x- > 1. 8. There exists a real number x such that a > 0 and a2 > 1. 9. For all real numbers x, if ac x. For all integers x, we find x+1 > x. For all irrational numbers xI we find x+1 > x. For all natural numbers x. we find 311: S 43:. For all rational numbers x. we find 33: S 4113. For all real numbers x, we find 3:!) S 4:13.. Question 10 [4 points) Select the following statements that are true. C] For all real numbers x we have x2 > 0. [:J For all natural numbers x we have x2 > 0. [:J For all integers x we have x2 > 0. C] There exists an integer x such that x2 = 2. C] There exists a natural number x such that x2 = 2. C] There exists a real number x such that x2 = 2. Question 11 (4 points) Let Q(x) be the statement "x + 1 > 2x." If the domain consists of all integers, select the following statements that are true. Q(0) Q(-1) Q(1) OFx, Q(x) (20)0'AO OFxc, -Q(20) (20) OL 'DAD Question 12 (4 points) Let Q(x) be the statement "a 0. For everya} E S, if x is less than 0, then x is even. For everym E S, if): is even. then a: g 0. For everva!) E S, if the ones digit of x is 2, then the tens digit is 3 or 4. For everym E S, if the ones digit of x is 6, then the tens digit is 1 or 2. Question 15 (4 points) Let S = {-48, -11. -8, 0. 10. 14. 16. 22. 26. 32. 42]. Select the following statements that are true. For everym E S, ifx is evenI then :1: Z 0.. For evervm E S, if x is less than 0, then x is even. For everym E S, if x is odd. then (B S 0. For everym E S, if the ones digit of x is 2. then the tens digit is 3 or 4. For everva} E S, if the ones digit of x is 6, then the tens digit is 1 or 2