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

Question

Let $A = 1, 2, 3$ . Then number of equivalence relations containing $(1, 2)$ is

1

2

3

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Daniel Discussed

Let

A = 1, 2, 3

. Then number of equivalence relations containing

(1, 2)

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

A = {1, 2, 3}

For equivalence relation containing

(1, 2)

For symmetric, it must consists

(1, 2)

and

(2, 1)

For transitivity, it must consists

(1, 3)

and

(3, 2)

and

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

For reflexivity, it must consists

(1, 1)

and

(2, 2), (3, 3)

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

\Rightarrow

Only

1

such relation is possible.

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Question Text	Let $A = 1, 2, 3$ . Then number of equivalence relations containing $(1, 2)$ is
Answer Type	Text solution:1
Upvotes	150