Answer to Question #326232 in Discrete Mathematics for John

Question

Let P ( x ) denote the sentence 2x + y = 5. What are the truth value of the following where the domain of x and y is the set of all integers.

1. Ɐx ⱯyP( x,y)

2. Ɐx ꓱyP ( x,y)

3. ꓱx ⱯyP ( x,y)

4. ꓱx ꓱyP( x,y)

Answer 1

1. False

Fore example P(0,1) is not correct $2x0+1 \not= 5$

2.True. Because for any x we can find value of y.

3.True. Because for any y we can find value of x.

4. True. Because for some x we can find some of y. For example P(0,5)

$2x0+5=5$