Kenneth Rosen Edition 7 Exercise 1.4 Question 11 (Page No. 53)

Question

Let $P(x)$ be the statement “$x = x^2$”. If the domain consists of the integers, what are these truth values?

1. $P(0)$
2. $P(1)$
3. $P(2)$
4. $P(-1)$
5. $\exists xP(x)$
6. $\forall x P(x)$

Answer 1

a) T, since 0 = 0^2

b) T, since 1 = 1^2

c) F, since 2 $\neq$2^2

d) F, since -1$\neq$ (-1)^2

e) T (let x=1)

f) F (let x=3)

Answer 2

Option a,b and e are true.