Total number of equivalence relation defined in the set $s = {a, b, c}$ is

5

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31

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2^{3}

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3^{3}

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Solution

The correct option is A $5$
By pascal's triangle
$1111311761115251011319065151$
Here no. of elements is $3$ .
$∴$ No. of equivalent relations $= 1 + 3 + 1 = 5$ .

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Similar questions

Q. Total number of equivalence relations defined in the set

S = {a, b, c}

is ?

Q. Let S be a relation on the set R of all real numbers defined by
S = {(a, b) ∈ R × R : a² + b² = 1}
Prove that S is not an equivalence relation on R.

Q. If

A

and

B

are two equivalence relations defined on set

C

, then

Q. Mark the correct alternative in the following question:

The relation S defined on the set R of all real number by the rule aSb iff a

\geq

b is

(a) an equivalence relation
(b) reflexive, transitive but not symmetric
(c) symmetric, transitive but not reflexive
(d) neither transitive nor reflexive but symmetric

On a set {a,b,c}, we define an equivalence relation 'R'. If this relation is {(a,a),(b,b),(c,c),(a,b),(b,a)}. How many equivalence classes will be formed from this relation?

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Total number of equivalence relation defined in the set s={a,b,c} is

The correct option is A 5By pascal's triangle1111311761115251011319065151Here no. of elements is 3.∴ No. of equivalent relations =1+3+1=5.

Total number of equivalence relation defined in the set $s = {a, b, c}$ is

The correct option is A $5$
By pascal's triangle
$1111311761115251011319065151$
Here no. of elements is $3$ .
$∴$ No. of equivalent relations $= 1 + 3 + 1 = 5$ .