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Question

Let X={1,2,3,4,5} and Y={1,3,5,7,9} . Which of the following is/are relations from X to Y?

A
R1={(x,y):y=2+x,xX,yY}
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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),(2,4),(7,9)}
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Solution

The correct options are
A R2={(1,1),(2,1),(3,3),(4,3),(5,5)}
C R3={(1,1),(1,3),(3,5),(3,7),(5,7)}
R1={(x,y):y=2+x,xX,yY}

x=1y=1+2=3
x=2y=2+2=4
x=3y=3+2=5
x=4y=4+2=6
x=5y=5+2=7

R={(1,3),(2,4),(3,5),(4,6),(5,7)}

Here in(4,6) ,6 does not belong to either XorY
So R1 is not a relation between X and Y

In R4, since it contains an element (7,9) which relates set Y to set Y, while rest elements relate set X to Y.
R4 is not a relation between X and Y



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