Mathematics Assignment | Custom Assignment Help
October 16th, 2019
1. (4 marks) Prove that for all sets A, B, and C,
A × (B ∩ C) = (A × B) ∩ (A × C).
2. (5 marks) Consider the function f : Z×Z → Z where f((x, y)) = 3x+ 5y for all (x, y) ∈ Z×Z.
(a) Is the function f one-to-one? Prove your answer.
(b) Is the function f onto? Prove your answer.
3. (8 marks) Let S = {(a1, a2, . . . , an)| n ≥ 1, ai ∈ Z
≥0
for i = 1, 2, . . . , n, an 6= 0}. So S is the set
of all finite ordered n-tuples of nonnegative integers where the last coordinate is not 0. Find a
bijection from S to Z
+.
4. (6 marks) Define a relation r on R as follows. For all a, b ∈ R, a r b if and only if abbaab < 0.
(a) Is r reflexive? Explain your answer.
(b) Is r symmetric? Explain your answer. Get mathematics assignment homework help today
