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Question

Let f:N×NN{1} be defined as f(m,n)=m+n, then function f is ______.

A
One-One and onto
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B
Many- One and not onto
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C
One- One and not onto
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D
Many- One and onto
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Solution

The correct option is D One-One and onto
Given f(m,n)=m+n
Range of this function is set of all natural numbers except 1
[since least value of m and n is 1]
Therefore the range and co-domain are equal
Therefore it is onto
For every (m,n), there exists only one m+n
Therefore it is one-one also
Hence, f is one-one and onto.

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