Question

Q. If a relation R on the set {1, 2, 3} be defined by R={(1, 1)}, then R is ?​

Answer 1

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R on the set {1,2,3} be defined by R={(1,2)}

It is clear that R is transitive.

a homogeneous relation R over a set X is transitive if for all elements a,b,c in X , whenever R relates a to b and b to c, then R also relates a to c.

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Answer 2

If a relation R on the set {1, 2, 3} be defined by R={(1, 1)}, then R is reflexive and symmetric

Given:

If a relation R on the set {1, 2, 3} be defined by R={(1, 1)},

To find:

R is what

Solution:

a = 1

b = 1

For a set to be reflexive (a,a)∈ R

In this case a is 1 and (1,1) ∈ R

So the condition holds true and it is reflexive.

For R to be symmetric,

(a,b) ∈ R and (b,a) ∈R

In this case, (a,b) = (1,1) which belongs to R

and (b,a) = (1,1) which also belogs to R

So, R is symmetric.

Hence R is symmetric and reflexive.

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