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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