Answer to Question #242320 in Discrete Mathematics for Amjad

Question

Let P(x) be the statement “x = x²." If the domain con- sists of the integers, what are these truth values? c) P(2) f) VxP(x) a) P(0) b) P(1) d) P(-1) e) 3x P(x)

Answer 1

c) $P(2):\,\,2 = {2^2}$

Since $2 \ne {2^2}$ , P(2) is false.

answer: false

d) $\forall xP(x)$ is false, since the condition $x = {x^2}$ is not satisfied for all x.

Answer: False

a) P(0)

Since $0 = {0^2}$ , P(0) is true.

Answer: True

b) P(1)

Since $1 = {1^2}$ , P(1) is true.

Answer: True

d) P(-1)

Since $-1 \ne {(-1)^2}$ , P(-1) is false.

Answer: False

e) $\exists xP(x)$ is true (condition $x = {x^2}$ is satisfied for $x=0, x=1$ )

Answer: True.