AP EAMCET · Maths · Functions
If \(f: \mathbf{N} \times \mathbf{N} \rightarrow \mathbf{N}\) is defined by \(f((m, n))=2^{m-1}(2 n-1), \forall(m, n) \in \mathbf{N} \times \mathbf{N}\), then \(f\) is
- A One-one but not onto
- B Onto but not one-one
- C Neither one-one nor onto
- D Both one-one and onto
Answer & Solution
Correct Answer
(D) Both one-one and onto
Step-by-step Solution
Detailed explanation
The given function \(f: \mathbf{N} \times \mathbf{N} \longrightarrow N\) is defined by \(f(m, n)=2^{m-1}(2 n-1), \forall(m, n) \in \mathbf{N} \times \mathbf{N}\). Now, let \(f((a, b))=f((c, d))\), where \(a, b, c, d \in \mathbf{N}\)…
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