Question

Let $X=\{0$, $1$, $2$, $3\}$ and $Y=\{-1$, $0$, $1$, $4$, $9\}$ and a function $f$ : $X\to Y$ defined by $y=x^2$, is

• A. one-one onto
• B. one-one into
• C. many-one onto
• D. many-one into

Answer 1

Answer: (B)

$y(0)=0$, $y(1)=1$, $y(2)=4$, $y(3)=9$. No two different values of $x$ (where $x\in x$) gives same image. Also $-1$ is element of set $Y$, which does not have its pre-image in set $X$. So, function is one-one into.