Answer to Question #265723 in Discrete Mathematics for loolie

Question

Determine the truth value of each of these statements if the domain for all variables consists of all integers. a) ∀n(n2 ≥ 0) b) ∃n(n2 = 2) c) ∀n(n2 ≥ n) d) ∃n(n2 < 0)

Answer 1

a) true

$n^2\ge0$ for all integers

b) false

if $n^2=2$ then $n=\pm \sqrt2$ is not integer

c) true

$n^2\ge n$ for all integers

d) false

$n^2>0$ for all n