Q154 / 270 · NDA 2022 (Phase 2) · Mathematics

Consider the following statements : 1. If $f$ is the subset of $Z \times Z$ defined by $f=\{(x y, x-y) ; x$, $y \in Z\}$, then $f$ is a function from $Z$ to $Z$. 2. If $f$ is the subset of $N \times N$ defined by $f=\{(x y, x+y)$; $x, y \in N\}$, then $f$ is a function from $N$ to $N$. Which of the statements given above is/are correct?

  • A
    1 only
  • B
    2 only
  • C
    Both 1 and 2
  • Correct answer
    D
    Neither 1 nor 2

Solution

For statement 1: Let $x y=6=1.6 \quad \Rightarrow x-y=1-6=-5$ and $x y=6=2.3 \quad \Rightarrow x-y=2-3=-1$ $\therefore 6$ related to both -5 and -1 So $f$ is not a function from $Z$ to $Z$. For statement 2 : Let $x y=6=1.6 \quad \Rightarrow x+y=1+6=7$ and $x y=6=2.3 \quad \Rightarrow x+y=2+3=5$ $\therefore \quad 6$ related to both 7 and 5 So $f$ is not a function from $N$ to $N$.

Hence, the correct answer is option: 'D'.

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