Let R = {(1, 2), (2, 3), (3, 3)} be a relation defined on the set {1, 2, 3, 4}. Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is: [2025]

Question

Let R = {(1, 2), (2, 3), (3, 3)} be a relation defined on the set {1, 2, 3, 4}. Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is: [2025]

Smart Achievers · Accepted Answer

(1)

Let A = {1, 2, 3, 4}

R = {(1, 2), (2, 3), (3, 3)} [Given]

For an equivalence relation 'R' should be reflexive, symmetric and transitive.

$∴$ Minimum elements that should be added are

(2, 1), (3, 2), (1, 1), (2, 2), (4, 4), (1, 3), (3, 1)

$∴$ Minimum number of elements required = 7.

Solution

Q.
Let R = {(1, 2), (2, 3), (3, 3)} be a relation defined on the set {1, 2, 3, 4}. Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is: [2025]

1 7

2 10

3 9

4 8

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Solution

Q. Let R = {(1, 2), (2, 3), (3, 3)} be a relation defined on the set {1, 2, 3, 4}. Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is: [2025]

1 7

2 10

3 9

4 8

Ans. (1) Let A = {1, 2, 3, 4} R = {(1, 2), (2, 3), (3, 3)} [Given] For an equivalence relation 'R' should be reflexive, symmetric and transitive. ∴ Minimum elements that should be added are (2, 1), (3, 2), (1, 1), (2, 2), (4, 4), (1, 3), (3, 1) ∴ Minimum number of elements required = 7.

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Q.
Let R = {(1, 2), (2, 3), (3, 3)} be a relation defined on the set {1, 2, 3, 4}. Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is: [2025]