Determine the truth value of each statement, assuming that x, y, and z are real numbers. Justify your answer. (a) ∀ x and y, ∃ z  x + y = z. (b) ∀ x ∃ y  ∀ z, x + y = z. (c) ∃ x  ∀ y, ∃ z  x z = y....

Determine the truth value of each statement, assuming that x, y, and z are real numbers. Justify your answer.

(a) ∀ x and y, ∃ z
 x + y = z.

(b) ∀ x ∃ y
 ∀ z, x + y = z.

(c) ∃ x
 ∀ y, ∃ z
 x z = y.

(d) ∀ x and y, ∃ z
 y z = x.

(e) ∀ x ∃ y
 ∀ z, z > y implies that z > x + y.

(f ) ∀ x and y, ∃z
 z > y implies that z > x + y.