Answer to Question #296210 in Discrete Mathematics for Jigger

Question

In general, a statement involving n variables x1 , x 2 ,…, x n can be denoted by P( x1 , x 2 ,…, x n ) and is the value of the predicate P at the n-tuple (x1 , x2 ,…, x n ) . (a) Suppose Q(x , y) denotes the statement “ x=y+3 .” What are the truth values of the propositions Q(1,2) and Q(3,0)? (b) Let R(x , y ,

Answer 1

(a) Suppose $Q(x , y)$ denotes the statement “$x=y+3$”. Let us find the truth values of the propositions $Q(1,2)$ and $Q(3,0).$ Since $1\ne 5=2+3,$ we conclude that the proposition $Q(1,2)$is false. Taking into account that $3=0+3,$ we conclude that the proposition $Q(3,0)$ is true.