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Let A = {1, 2, 3 }. Then number of relations containing (1, 2

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Let $A = {1, 2, 3}$ . Then number of relations containing $(1, 2)$ and $(1, 3)$ which are reflexive and symmetric but not transitive is

1

2

3

4

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Let

A = {1, 2, 3}

. Then number of relations containing

(1, 2)

and

(1, 3)

which are reflexive and symmetric but not transitive is

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

Total possible pairs

= {(1, 1), (1, 2), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}

Reflexive means

(a, a)

should be in relation.So

(1, 1), (2, 2), (3, 3)

should be in a relation.

Symmetric means if

(a, b)

is in relation,then

(b, a)

should be in relation.

So,since

(1, 2)

is in relation,

(2, 1)

should be in relation and since

(1, 3)

should be in relation.

Transitive means if

(a, b)

is in relation,and

(b, c)

is in relation,then

(a, c)

is in relation.

If we add

(2, 3)

,we need to add

(3, 2)

for symmetric,but it could become transitive then

Relation

R 1 = {(1, 1), (1, 2), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}

So,there is only

1

possible relation.

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Question Text	Let $A = {1, 2, 3}$ . Then number of relations containing $(1, 2)$ and $(1, 3)$ which are reflexive and symmetric but not transitive is
Answer Type	Text solution:1
Upvotes	150

Let A={1,2,3}. Then number of relations containing (1,2) and (1,3) which are reflexive and symmetric but not transitive is

Text solutionVerified

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Let $A = {1, 2, 3}$ . Then number of relations containing $(1, 2)$ and $(1, 3)$ which are reflexive and symmetric but not transitive is