**Proof:** **For all a ∊ R, (a, a) ∊ R. Since R is reflexive. So according to problem **

**(a, a) ∊ T.**

**Suppose (a, b) ∊ T.**

**Then by problem (a, b) ∊ R and (b, a) ∊ R**

**⇒ (b, a) ∊R and (a, b) ∊R**

**⇒ (b, a)∊ T.**

**Let (a, b) ∊ T and (b, c) ∊ T, then by problem (a, b) ∊ R and (b, c) ∊ R**

**And (b, c) ∊ R and (c, a) ∊ R.**

**⇒ (a, b) ∊ R and (b, c) ∊ R and (c, b) ∊ R and (b, a) ∊ R**

**⇒ (a, c) ∊ R and (b, a) ∊ R**

**Then T is transitive.**

**Therefore T is equivalence relation**.**(proved)**

Home / Discrete mathematics / Let R be a transitive reflexive relation on A. Let T be a relation on A such that (a, b) ∊T if and only if both (a, b) ∊ T and (b, a) ∊ R. Show that T is equivalence relation.

Tags Discrete mathematics Equivalence relation mathematics Transitive relation

### Check Also

## Procedure for computing shortest distance| Discrete Mathematics

Solution: The procedure for computing the shortest distance/path from a to any vertex G. Initially, ...