Determine whether the following functions are injective, or surjective, or neither injective nor surjective.
a) f ∶ {a, b, c, d} → {1, 2, 3, 4, 5} given by f (a) = 2, f (b) = 1, f (c) = 3, f (d) = 5. Is f injective? Is f surjective?
b) f ∶ R → R by f (x) = x + 1. Is f injective? Is f surjective?
c) f ∶ Z × Z → Z by f (m, n) = m + n. Is f injective? Is f surjective?
d) f ∶ Z × Z → Z by f (m, n) = m2 + n 2 . Is f injective? Is f surjective?
