Hello, if you have any need, please feel free to consult us, this is my wechat: wx91due

CMPSC 360, Discrete Mathematics for Computer Science, HW 6

4. Let T = {10, 15,20,25,30}. Define a relation Ron T by aRb if |a - b| = 5k for some integer k.

(a) Find the equivalence classes of R.

(b) List all elements in each equivalence class of R and explain your reasoning.

(c) How many distinct equivalence classes does R have? Provide justification for your answer.

(d) If we define a new set T' = {10,15,20,25,30,35} and use the same relation R, will the number of equivalence classes change? Explain why or why not.        (20 pts)

5. Consider the relation R defined on Z × Z:

Prove that R is an equivalence relation on Z × Z.            (20 pts)

6. Consider the piecewise function f: (-5, 5) → R defined as  (16 pts)

(a) Determine the domain and co-domain of f.

(b) What is the range/image of f?

(c) Prove or disprove whether f is injective (one-to-one).

(d) Prove or disprove whether f is surjective (onto).