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Question

# Let A={x: x=2n+1,n∈W} and B={y: y=2n,n∈N}. If a relation R is defined from A to B, then which of the following is void relation?

A
R={(x,y):x+y=11}
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B
R={(x,y):x+2y=21}
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C
R={(x,y):2x+y=14}
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D
R={(x,y):x+y=8}
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Solution

## The correct option is D R={(x,y):x+y=8}A={x: x=2n+1,n∈W} ⇒A={1,3,5,7,9,...} B={y: y=2n,n∈N} ⇒B={2,4,6,8,10,...} R={(x,y):x+y=11} Here, R={(1,10),(3,8),(5,6),(7,4),(9,2)} It is not a void relation. R={(x,y):x+2y=21} Here, R={(1,10),(5,8),(9,6),(13,4),(17,2)} It is not a void relation. R={(x,y):2x+y=14} Here, R={(1,12),(3,8),(5,4)} It is not a void relation. R={(x,y):x+y=8} Since, x is odd number and y is even number, so sum of x+y can never be even number. Hence, it is a void relation.

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