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

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

(a) ∃ x
 ∀ y ∃ z
 x + y = z.

(b) ∃ x and y
 ∀ z, x + y = z.

(c) ∀ x and y, ∃ z
 y – z = x.

(d) ∀ x and y, ∃ z
 x z = y.

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

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