TS EAMCET · Maths · Functions
For each \(n \in \mathbf{N}\), let \(A_n=\{(n+1) k / k \in \mathbf{N}\}\) and \(X=\bigcup_{n \in \mathbf{N}} A_n \cdot A\) mapping \(f: X \rightarrow N\) defined by \(f(x)=x, \forall x \in \mathbf{X}\), is
- A one-one and onto
- B one-one but not onto
- C onto but not one-one
- D neither one-one nor onto
Answer & Solution
Correct Answer
(B) one-one but not onto
Step-by-step Solution
Detailed explanation
Given that, \(A_n=\{(n+1) k \mid k \in \mathbf{N}\}\) If \(n=1, A_1=\{2 k \mid k \in \mathbf{N}\}\) for, \(k=1,2,3 \ldots A_1=\{2,4,6,8, \ldots\}\) If \(\quad n=2, A_2=\{3 k \mid k \in \mathbf{N}\}\) for \(\quad k=1,2,3, \ldots \quad A_2=\{3,6,9, \ldots\}\) If…
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