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Question

If X={1,2,3,4,5},Y={1,3,5,7,9}, then which among the following is not a relation from X to Y 


A
R1={(x,y):y=x+2;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),(2,1)(2,5),(3,7),(7,9)}
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Solution

The correct option is D R4={(1,3),(2,1)(2,5),(3,7),(7,9)}
We have,
R1={(x,y):y=x+2;xX,yY}
={(1,3),(3,5),(5,7)}
so, we can say that, R1,R2,R3 are subsets of X×Y

In R4, we have (7,9) 
but (7,9)X×Y, because 7 is not an element of set X. So, R4 is not a subset of X to Y
R4 is not a relation from  X to Y

Mathematics

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