Question

Let A= {2,4,6,8} and R be relation "is greater than" on set a
i) Write the set as ordered pairs
ii) check if relation is reflexive, justify.
iii) check if it's symmetric, justify
iv) check if R is an equivalence relation, justify

Answer 1

Step-by-step explanation:

Given:Let A= {2,4,6,8} and R be relation "is greater than" on set A.

To find:

i) Write the set as ordered pairs

ii) check if relation is reflexive, justify.

iii) check if it's symmetric, justify

iv) check if R is an equivalence relation, justify

Solution:

i) Write the set as ordered pairs:

Ans:

R={a 'greater than 'b}

R={(4,2),(6,2),(8,2),(6,4),(8,6),(8,4)}

ii) check if relation is reflexive, justify.

Ans:

A relation is reflexive if (a,a) belongs to R

here in R

R={(4,2),(6,2),(8,2),(6,4),(8,6),(8,4)}

No such ordered pair exists,because any number is not greater then itself.

So,R is not reflexive.

iii) check if it's symmetric, justify

Ans:A relation is symmetric if (a,b) belongs to R,

then (b,a) belongs to R.

here in R

R={(4,2),(6,2),(8,2),(6,4),(8,6),(8,4)}

No such ordered pair exists,because if a>b,then b is not greater than a.

So,R is not Symmetric.

iv) check if R is an equivalence relation, justify

Ans:A relation is equivalence relation

if,

R is reflexive,symmetric and transitive

from (ii) and(iii) it is clear that the relation R is neither reflexive nor symmetric, hence we need not to check for transitivity; as the given relation is not equivalence relation.

Hope it helps you.

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