Question

Consider the following statements
Statement I Let $f$ be the subset of $Z\times Z$ defined by $f=\{(ab,a+b):a,b\in Z\}$. Then, $f$ is a function from $Z$ to $Z$.
Statement II Let $A=\{9,10,11,12,13\}$ and let $f:A\to N$ 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, $f(ab)=a+b\forall a,b\in Z$
$f(0\times 2)=0+2$
$f(0)=2$
$f(0\times 5)=0+5$
$f(0)=5$
$\because 0$ has more than one image.
$\therefore f$ is not a function from $Z$ to $Z$.
II. Now, $A=\{9,10,11,12,13\}$
$f:A\to N,f(x)=$ The highest prime factor of $x$
$\therefore t=\{(9,3),(10,5),(11,11),(12,3),(13,13)\}$
$\therefore$ Range of $f=\{3,5,11,13\}$