KVPY 2020-21 SB SX Exam Previous Papers

Question : 84 of 120

Marks: +1, -0

Let

{A}

be a set consisting of 10 elements. The number of non-empty relations from A to A that are reflexive but not symmetric is

Solution:

{n}({A} \×{A})=100

number of (a,a) type pairs is 10 number of

(a, b)

and

(b, a)

type pair of pairs is

45(a \≠b)

so, required number of relations is

2^{90}-2^{45}

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