Question

Consider the following statements
Statement I Let $f$ be the subset of $Z \times Z$ defined by $f=\{(a b, a+b): a, b \in Z\}$. Then, $f$ is a function from $Z$ to $Z$.
Statement II Let $A=\{9,10,11,12,13\}$ and let $f: A \rightarrow N$ be defined by $f(x)=$ The highest prime factor of $n$. Then, the range of $f$ is $\{2,3,5\}$. Choose the correct option.

• A. Statement 1 is true
• B. Statement II is true
• C. Both are true
• D. Both are false

Answer 1

Answer: (D)

I. We have, $f(a b)=a+b \forall a, b \in Z$
$f(0 \times 2) =0+2 $
$f(0) =2 $
$f(0 \times 5) =0+5$
$f(0) =5$
$\because 0$ has more than one image.
$\therefore f$ is not a function from $Z$ to $Z$.
II. Now, $A=\{9,10,11,12,13\}$
$f: A \rightarrow N, f(x)=$ The highest prime factor of $x$
$\therefore t=\{(9,3),(10,5),(11,11),(12,3),(13,13)\}$
$\therefore$ Range of $f=\{3,5,11,13\}$