(a) The square root of an integer is a non negative real number.
(b) There is an angle $\alpha$ that $\sin \alpha = \cos \alpha$.
(c) $x<1$.
(d) If $x<1$, then $x^{2}<1$.
(e) If $x$ is an arbitrary complex number, then $x^{2}-x=1$.
Ambiguous means that its validity or falsity depends on the value of the variables x and y.
A) False
B) True. (Understanding an angle such as "at least one angle", not "a single angle".
C) Ambiguous.
D) False.
E) False.
(A) is false, because there are integers whose square roots are complex numbers; for example, $-1$.
(B) is true; $\alpha = 45^{\circ}$ is sufficient.
(C) is ambiguous; to show this, you just need to find an $x$ so that $x < 1$ and another so that $x \nless 1$. I'll leave it to you to find those examples.
(D) is false; to prove it, you need an $x < 1$ with $x^2 \geq 1$. Think about extreme cases - in particular, don't limit yourself to positive values of $x$.
(E) is extremely false. Pick a value of $x$ at random, and check whether $x^2 - x = 1$. If not, you have your counterexample. (It's extremely unlikely that you'll pick a value of $x$ for which $x^2 - x = 1$.)