Question

If $A=\left\{\begin{array}{c}x\in R:x^2+6x-7<0\end{array}\right\}$ and $B=\left\{\begin{array}{c}x\in R:x^2+9x+14<0\end{array}\right\}$, then which of the following is/are correct?
1. $(A\cap B)=(-2,1)$
2. $(A\setminus B)=(-7,-2)$
Select the correct answer using the code given below :

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

Answer 1

Answer: (D)

Neither 1 nor 2

Solution:

We have, $A=\{x\in R:x^2+6x-7<0\}$ and

$B=\{x\in R:x^2+9x+14<0\}$

$\therefore A=\{x\in IR:(x-1\left)\right(x+7)<0\}$ and

$B=\{x\in IR:(x+2\left)\right(x+7)<0\}$

$A=(-7,1)$ and $B=(-7,-2)$

$(A\cap B)=(-7,-2)$

$(A\setminus B)=[-2,1)$

Hence, D is the correct option.