Answer
Done below.
Work Step by Step
a) For all real $x$, $x^2$ does not equal -1. This is true.
b) There exists an integer $x$ such that $x^2$ equals 2. This is false, as $x$ would have to be irrational.
c) For all integers $x$, $x^2 > 0$. This is false, since $x = 0$ is a counterexample.
d) There exists a real number $x$ such that $x^2$ equals $x$. This is true (take $x = 1$).
