Discrete Math. (Relations)

timer Asked: Nov 10th, 2016

Question description

1. Let A = {1, 2, 3, 4, 5} and define r on A by xry if |x - y| <= 1.

We define r2 = rr and r3 = r2r.

Give the Boolean matrix for:

(a) the relation r,

(b) the relation r2,

(c) the relation r3.

2. a. Prove that conguence modulo m is a transitive.

(b) What are the equivalence classes under conguence modulo 2?

(c) What are the equivalence classes under conguence modulo 10?

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