Q13 of 109 Page 1

Define an equivalence relation.

A relation R on a set A is said to be an equivalence relation on A iff:


1. Its reflexive i.e (a,a) ∈ R ∀ a ∈ A


2. Its symmetric i.e (a,b) ∈ R → (b,a) ∈ R ∀ a,b ∈ A


3. Its transitive i.e (a,b) ∈ R and (b,c) ∈ R → (a,c) ∈ R ∀


a,b,c ∈ A


More from this chapter

All 109 →
11

Define a symmetric relation.

 12

Define a transitive relation.

 14

If A = {3, 5, 7} and B = {2, 4, 9} and R is a relation given by “is less than”, write R as a set ordered pairs.

 15

A = {1, 2, 3, 4, 5, 6, 7, 8} and if R = {(x,y) : y is one half of x; x, y ϵA} is a relation on A, then write R as a set of ordered pairs.