AP EAMCET Engineering 22 Sep 2020 Shift 2 Paper

The given function f:N×N⟶N is defined by f(m,n)=2m−1(2n−1),∀(m,n)∈N×N
Now, let f((a,b))=f((c,d)), where a,b,c,d∈N
⇒2a−1(2b−1)=2c−1(2d−1)
⇒2a⋅b−2a−1=2c⋅d−2c−1⇒(a,b)=(c,d)
∴f is a one-one function.
Now as 2m−1 is a even number for ∀m∈N−{l} and (2n−1) is a odd number for ∀N∈N, so the every natural number can be obtain by the for 2m−1.(2n−1) for some combination of (m,n), so f is an onto function.