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Question

For real numbers x and y, we define xRy if xy+5 is an irrational number. The relation R is

A
Reflexive
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B
Symmetric
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C
Transitive
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D
None of these
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Solution

The correct option is A Reflexive
xϵRxx+5=5 is an irrational number.
(x,x)ϵR

Hence, R is reflexive
(5,1)ϵR because 51+5=251
which is an irrational number.
(1,5/ϵR

Hence, R is not a symmetric

We have, (5,1)(1,25)ϵR because
51+5=251, if
125+5=15 are irrational number.

(5,25)/ϵR

Hence, R is not transitive.

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