et SCN be the set that contains exactly all prime numbers, and let RC S x S be the relation efined by the rule (x, y) ER⇒ x - y = 2. (a) Prove or find a counterexample for the following properties: • antisymmetry • asymmetry • symmetry ● irreflexivity • reflexivity • transitivity • uniqueness

Q: Do question 3 only

A: Step 1: Step 2: Step 3: Step 4:

Q: Exercise 1. Let R = {(x, y) | x, y E Z and x + y = 0, } be a relation on Z. Prove or disprove if R…

A: Let S be a non-empty set and R be a binary relation on S. (a) The relation R is said to be reflexive…

Q: 4. Define a relation R on N by aRb if a and b have no common factors except 1. (a) Give an example…

A: We have define  a relation R on natural numbers (N) by aRb if a and b have no common  factors except…