Question

If $A=\{3,5\}$ and $A\times B=B\times A$, then the correct option(s) can be

• A. $B=\{x:x^2-8x+15=0\}$
• B. $B=\{x:|x-4|=1\}$
• C. $B=\{x:x\text{is prime factor of}15\}$
• D. $B=\{x:x\in N,3\le x\le 5\}$

Answer 1

Answer: (A), (B), (C)

$B=\{x:x\text{is prime factor of}15\}$

Here, $A\times B=B\times A⟹A=B$
$B=\{x:x^2-8x+15=0\}$
$\Rightarrow x^2-8x+15=0$
$\Rightarrow x^2-3x-5x+15=0$
$\Rightarrow (x-3)(x-5)=0$
​​​​​​​​​​​​​​​​​​​​​$\Rightarrow x=3,5$
$B=\{3,5\}$

$B=\{x:|x-4|=1\}$
$\Rightarrow |x-4|=1$
$\Rightarrow x-4=\pm 1$
​​​​​​​$\Rightarrow x=3,5$
$B=\{3,5\}$

​​​​​​​$B=\{x:x\text{is prime factor of}15\}$
Factors of $15$ is $\{1,3,5,15\}$
Prime factors are $\{3,5\}$
$B=\{3,5\}$

$B=\{x:x\in N,3\le x\le 5\}$
$\Rightarrow x=3,4,5$
​​​​​​​$B=\{3,4,5\}$