AP EAMCET202022 Sep 2020Evening ShiftMathematicsFunctionsActual
If f: N N N is defined by f((m, n))=2^ m-1 (2 n-1), (m, n) N N , then f is
Options
- AOne-one but not onto
- BOnto but not one-one
- CNeither one-one nor onto
- DBoth one-one and onto
Correct answer
D. Both one-one and onto
Step-by-step solution
The given function f: N N N is defined by f(m, n)=2^ m-1 (2 n-1), (m, n) N N . Now, let f((a, b))=f((c, d)) , where a, b, c, d N aligned & 2^ a-1 (2 b-1)=2^ c-1 (2 d-1) & 2^a b-2^ a-1 =2^c d-2^ c-1 (a, b)=(c, d) aligned f is a one-one function. Now as 2^ m-1 is a even number for m N - 1 and (2 n-1) is a odd number for N N , so the every natural number can be obtain by the for 2^ m-1 (2 n-1) for some combination of (m, n) , so f is an onto function. Hence, option (4) is correct.