Let the set of all relations R on the set { a , b , c , d , e , f } , such that R is reflexive and symmetric, and R contains exactly 10 elements, be denoted by S . Then the number of elements in S is

Question

Let the set of all relations R on the set { a , b , c , d , e , f } , such that R is reflexive and symmetric, and R contains exactly 10 elements, be denoted by S . Then the number of elements in S is ______

TestHub · Accepted Answer

For relation to be reflexive all the diagonal elements must be taken and out of remaining 30 elements there are 15 pairs and we need 2 pairs such that R contains exactly 10 elements and is both reflexive and symmetric. $∴$ number of ways $=^{15} C_{2} = 105$

Mathematics - Sets and Relations Question with Solution | TestHub

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