Define a function, R : R 2 P 4 [ R (a, b)](x) = (x 2 - a 2 )(x 2 - b 2 ) (a) Is R injective? Prove your answer. (b) Is R surjective?

Define a function, R: R2 → P4

[R(a, b)](x) = (x2 - a2)(x2 - b2)

(a) Is R injective? Prove your answer.

(b) Is R surjective? Prove your answer.

(c) Given an example of a set, Y, so that: Y⊆P4, Y contains at least 5 distinct elements, and R is

surjective when redefined to be R: R × {0} → Y.