Chapter 1.5, Problem 27E

Determine the truth value of each of these statements if the domain for all variables consists of all integers.

a) $\forall n\exists m\left(n^2<m\right)$

b) $\exists n\forall m\left(n<m^2\right)$

c) $\forall n\exists m\left(n+m=0\right)$

d) $\exists n\forall m\left(nm=m\right)$

e) $\exists n\exists m\left(n^2+m^2=5\right)$

f) $\exists n\exists m\left(n^2+m^2=6\right)$

g) $\exists n\exists m\left(n+m=4\wedge n-m=1\right)$

h) $\exists n\exists m\left(n+m=4\wedge n-m=2\right)$

i) $\forall n\forall m\exists p\left(p=\left(m+n\right)/2\right)$