6. Determine whether f : Z × Z → Z is onto ifa) f (m, n) = 2m − n b) f (m, n) = m2 − n2 c) f (m, n) = m + n + 1d) f (m, n) = |m| − |n| e) f (m, n) = m2 − 4 f) f (m, n) = m + n

Which of the following function f: Z X Z → Z is not onto?a.f(a, B) = a – bb.f(a, B) = |b|c.f(a, B) = a + bd.f(a, B) = a

4. Determine whether each of these functions from {a, b, c, d} to itself is one-to-one (onto)a) f (a) = b, f (b) = a, f (c) = c, f (d) = db) f (a) = b, f (b) = b, f (c) = d, f (d) = cc) f (a) = d, f (b) = b, f (c) = c, f (d) = d

Prove.(a) f : Z+ → Z+, f (x) = 2x + 1 is one-to-one.(b) f : Z+ → Z, f (x) = 2x − x2 is not one to one.(c) f : R \ {0} → R+, f (x) = 1x2 is onto.(d) f : Z+ → Z+, f (x) = 2x − 1 is not onto.

Let A=7,8,9 and B=7,8,9 and f is onto from A to B, then which of the following is correct?*f is bijectivef is surjectivef may or may not be bijectivef is into function

For each of the following functions, state whether it is injective, surjective, and/or bijective, and why.(a) The function f (n) = 2n, mapping from integers to integers.(b) The function q(ϕ), with codomain N≥0, which maps any formula of predicate logic to the number of quantifiersin that formula