MAT1830
Which of the following sentences is logically equivalent to VxyPx,yAQxy
Consider the sentences VxyPx,yand yVxPxy. Are these sentences true or false under the interpretation where x and y range over the positive integers and Px,yis 2x=y+1?
OVxyPx,yA-Qx,y
OVxyPx,y is true, yVxPxy is true
O Vx3y(-P(x,y)V-Q(x,y)) O3xVy-Px,yA-Qxy
OVxyPxy is true, yVxPxy is false
OVxyPxy is false, yVxPxy is true
O3xVy-P(x,y)VQ(x,y))
OVxyPx,y is false, yVxPx,y is false
Consider the sentence xPxAxQx-xPxAQx. Which of the following is true?
Consider the sentences VxyPx,y and yVxPx,y. Are these sentences true or false under the interpretation where x and y range over the integers and Px,y is "y + 4x is even?
O A. The sentence is valid.
OVxyPxy is true, yVxPxy is true
O B. The sentence is not valid. It is false under the interpretation where x ranges over the integers, Px is x16 and Qx is x is negative
OVxyPxy is true, yVxPxy is false
OVxyPxy is false, yVxPxy is true
O C. The sentence is not valid. It is false under the interpretation where x ranges over the integers, Px is x-16 and Qx is 2x4
OVxyPx,y is false, yVxPx,y is false
O D. The sentence is not valid. It is false under the interpretation where x ranges over the integers, Px is x216 and Qx is 1x3
-<3n for all integers n 5, the base step would consist of proving which of the following inequalities? 6 Suppose you know the following about a statement P(n) O+++++33 P4, P8, and P12 are all true. 0+++++< P1 and P3 are false. For all integers k5, if Pk is true then Pk +1 is true 0+ What is the smallest integer x for which you can be sure that Pn is true for all integers nx? <++++f+f0 O++++++15 Answer:
