Can someone please provide a step-by-step explanation for the answer?

If the universe of discourse is the real numbers, give the truth value of each of the
following propositions:

(a) ∀x∃y(x = y²)
(b) ∀x∃y(x² = y)
(c) ∃x∀y(xy = 0)
(d) ∀x∃y(x + y = 1)