GATE | GATE CS 2020 | Question 27

Let R be the set of all binary relations on the set {1, 2, 3}. Suppose a relation is chosen from R at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is ________ .

**Note –** This question was Numerical Type.**(A)** 0.125**(B)** 0.25**(C)** 0.50**(D)** 0.625**Answer:** **(A)****Explanation:** The probability that the chosen relation is reflexive on a set with n elements:

= (number of reflexive relations) / (total number of relations) = (2^{n2}-^{n}) / (2^{n2})

Given, size (number of elements) of set is 3 (i.e., {1, 2, 3}). Therefore,

= (2^{32}-^{3}) / (2^{32}) = (2^{6}) / (2^{9}) = 1 / (2^{3}) = 1 / 8 = 0.125

Option (A) is correct.

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