Determine the truth values of the following statements. (assume that x and y are real numbers)
a) the product xy = 0 if and only if either x = 0 or y = 0.
b) the sum of squares x^2 + y^2 > 1 iff both x and y are greater than 1.
c) x^2 − 4x + 3 = 0 ⇔ x = 3
d) x^2 > y^2 ⇔ x > y