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Question

# If X={1,2,3,4,5} and Y={1,3,5,7,9} then which of the following sets are relation from X to Y

A
R1={(x,a):a=x+2,xX,aY}
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B
R2={(1,1),(2,1),(3,3),(4,3),(5,5)}
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C
R3={(1,1),(1,3),(3,5),(3,7),(5,7)}
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D
R4={(1,3),(2,5),(4,7),(5,9),(3,1)}
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Solution

## The correct options are B R2={(1,1),(2,1),(3,3),(4,3),(5,5)} C R3={(1,1),(1,3),(3,5),(3,7),(5,7)} D R4={(1,3),(2,5),(4,7),(5,9),(3,1)}R1={(1,3),(2,4),(3,5),(4,6),(5,7)}since 4 and 6 do not belong to y.∴(2,4),(4,6)∉R1∴R1={(1,3),(3,5),(5,7)}⊂X×YHence, R1 is a relation but not a mapping as the elements 2 and 4 do not have any image.R2: It is certainly a mapping and since every mapping is a relation, it is a relation as well.R3: It is a relation being a subset of X×Y.R4: It is both mapping and a relation. Each element in X has a unique image. It is also one-one and on-to mapping and hence a bijection.

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