Q. 1A4.1( 535 Votes )

# Determine whether each of the following relations are reflexive, symmetric and transitive:

Relation R in the set A = {1, 2, 3, ..., 13, 14} defined as

R = {(x, y) : 3x – y = 0}

Answer :

It is given that Relation R in the set A = {1, 2, 3, ..., 13, 14} defined as

R = {(x, y) : 3x – y = 0}

Then, R = {(1,3), (2,6), (3,9), (4,12)}

__REFLEXIVE__**A**relation is said to be reflexive if (x, x) ϵ R, where x is from domain.

R is not reflexive as (1,1), (2,2) …… (14,14) ∉ R

**SYMMETRIC**

A relation is said to be symmetric if (y, x) ϵ R whenever (x, y) ϵ R.

Also, R is not symmetric as (1,3) ϵ R, but (3,1) ∉ R

**TRANSITIVE**

A relation is said to be transitive if (x, z) ϵ R whenever (x, y) ϵ R and (y, z) ϵ R

And, also R is not transitive as (1,3), (3,9) ϵ R, but (1,9) ∉ R

Therefore, R is neither reflexive, nor symmetric, nor transitive.

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