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Question

Let N denote the set of all natural numbers. Define two binary relations on N as
R1={(x,y)N×N:2x+y=10} andR2={(x,y)N×N:x+2y=10}. Then

A
Both R1 and R2 are transitive relations.
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B
Range of R2 is {1,2,3,4}.
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C
Range of R1 is {2,4,8}.
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D
Both R1 and R2 are symmetric relations.
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Solution

The correct option is B Range of R2 is {1,2,3,4}.
R1={(1,8),(2,6),(3,4),(4,2)}R2={(8,1),(6,2),(4,3),(2,4)}Range of R2={1,2,3,4}

(1,8)R1 but (8,1)R1, so R1 is not symmetric.
(4,2)R1 & (2,6)R1 but (4,6)R1, So R1 is not transitive.

Similarly, R2 is neither symmetric nor transitive.

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