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Question

If A={1,2,3,4}, then which among the following relations are not functions from A to itself

A
f1={(x,y)|y=x+1, x,yA}
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B
f2={(x,y)|x+y>4, x,yA}
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C
f3={(x,y)|y<x, x,yA}
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D
f4={(x,y)|x+y=5, x,yA}
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Solution

The correct option is C f3={(x,y)|y<x, x,yA}
f1={(x,y)|y=x+1, x,yA}
f1={(1,2),(2,3),(3,4)}
Since element 4 is mapped to 5 according to relation but 5A, it is not a function.

f2={(x,y)|x+y>4, x,yA}
f2={(1,4),(2,3),(2,4),(3,3),(3,4),(4,4),(4,1),(3,2)(4,2),(4,3)}
Since for x=2, there are two mappings. So, it is not a function.

f3={(x,y)|y<x, x,yA}
f3={(2,1),(3,1),(3,2)}
Since for x=3, there are two mappings. so, it is not a function.

f4={(x,y)|x+y=5, x,yA}
f4={(1,4),(2,3),(3,2),(4,1)}
Since, Domain ={1,2,3,4}
Since, every element in A is associated to a unique element in A.
Therefore, it is a function from A to itself.

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