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Question

Let R be a relation on the set of natural numbers N defined by xRy iff 2x+3y=21. Then 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 D None of these
2x+3y=21

(i) Reflexive :
Let xRx
2x+3x=21
5x=21x=215N
R is not reflexive.

(ii) Symmetric :
Let xRy
2x+3y=21
(9,1)R but (1,9)R
R is not symmetric.

(iii) Transitive :
(6,3),(3,5)R but (6,5)R
R is not transitive.

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