Answer to Question #349296 in Discrete Mathematics for nouman

Question

Question 1: Let R be a relation in a set A, and derive from R another relation S in A as follows:

x S y if (x R y or y R x).

a) Prove that if R is reflexive, then S is reflexive.

b) Prove that S is symmetric.

c) Prove that if R is transitive, S is not necessarily transitive (by a counterexample).

d) If R is antisymmetric, is S antisymmetric? Prove your answer.

e) If R is an equivalence relation, is S an equivalence relation? Prove your answer.

f) If R is a partial order, is S a partial order? Prove your answer.

Answer 1

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