answer (e.g., if you claim that a function is invertible,
) Consider the following functions. Decide whether these functions are injective,
surjective, and invertible. Justify your answer (e.g., if you claim that a function is invertible, you need to
give a justification as to why you think that function is invertible). Give counterexamples when needed.
You can draw arrow diagrams to help justifying your answer.
a) Function f: ℤ × ℤ → ℤ is defined as f((a, b)) = 2b – 4a.
b) A = {1, 2, 3}. Function f: ?(A) → {0, 1, 2, 3} is defined as f(X) = |X| where |X| = size of X. For
example, |{1, 2}| = 2. ?(A) is the power set of A.
c) Function f: {0, 1}3 → {0, 1}3 is defined by the following rule. For each string s ∈ {0, 1}3,
f(s) = f(x1x2x3) = x3x1x2, where x1, x2, x3 ∈ {0, 1}. For example, if x1 = a, x2 = b, and x3 = c, then
f(abc) = cab. Another example: f(011) = 101.
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