The number of equivalence relations defined on set A={a,e,i,o,u} is k then the sum of the digits in k is

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The number of equivalence relations defined on set $A = {a, e, i, o, u}$ is $k$ then the sum of the digits in $k$ is

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answer is 7.

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Detailed Solution

1
1 2
2 3 5

5 7 10 15

15 20 27 37 52

52 67 87 114 151 203

In this triangle, the last number in the sixth row (203) represents the number of equivalence relations defined on a set with 6 - 1 = 5 elements.

Therefore the number of equivalence relations $= 52$

$∴ x + y = 7$

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