Kenneth Rosen Edition 7 Exercise 1.4 Question 52 (Page No. 56)

Question

As mentioned in the text, the notation$\exists \sim xP (x)$ denotes “There exists a unique $x$ such that $P(x)$ is true.”If the domain consists of all integers, what are the truth values of these statements?

1. $\exists \sim x(x>1)$
2. $\exists \sim x (x^2 = 1)$
3. $\exists x (x+3 = 2x)$
4. $\exists \sim x(x = x+1)$

Answer 1

Option c is true.