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)
= (2n2-n) / (2n2) 

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

= (232-3) / (232) 
= (26) / (29)
= 1 / (23)
= 1 / 8
= 0.125 

Option (A) is correct.

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