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JEE MainMathematicsSets and Relations

Let A = 1, 2, 3, 4, 5 . The number of equivalence relations on A that contain the ordered pair (1, 2) but do not contain the ordered pair (4, 5) is ______.

Correct answer

10

Step-by-step solution

Let A = 1, 2, 3, 4, 5 . We need to find the number of equivalence relations on A containing (1, 2) but not (4, 5) . Every equivalence relation on a set corresponds to a unique partition of that set. The condition that the relation contains (1, 2) means that elements 1 and 2 must be in the same block of the partition. We can treat 1, 2 as a single merged element. The set then effectively becomes a 4 -element set: 1, 2 , 3, 4, 5 . The total number of equivalence relations containing (1, 2) is equal to the number of p

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