Question

let R be the relation on W(set of whole numbers) defined by R={(x, y) : x, y€ W, 3x+2y=12} check the Relation R for reflexive, symmetric and transitive.​

Answer 1

Answer:

given:-x,y€W

=x€W,y€W

R=[(x,y):x,y€W,3x+2y=12]

at x=1,y=9/2

at x=2,y=3

at x=3,y=2/3

Answer 2

Concept introduction:

relationship between two numbers and characteristics are often calculated through the application of permutation and combination.

Given:

We have been given the values of R and Y.

To find:

We have to find the relation of R for reflexive and translative.

Solution:

According to the question,

A binary relation is said to be an equivalence relation if it is reflexive, symmetric and transitive.

For Reflexivity:

a∼a.

For Symmetric: If

a∼b,thenb∼a.

For Transitive: If

a∼bandb∼cthena∼c.

Instruction Check whether the given relation is reflexive or not.

Calculation Here,

R={(x,y):x,y∈W,3x+2y=12}.

This implies,

y=12−3x2.

So,

R={(0,6),(1,92),(2,3),(3,32),(4,0)}

But

92,and32

are not whole numbers. So, the relation becomes,

R={(0,6),(2,3),(4,0)}.

By reflexive property,

(x,x)∈R.

But in R there is no such relation.

Final answer:

Hence, the given relation is not reflexive.

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