Question

If $A=\left\{a,b,c\right\},B=\left\{b,c,d\right\}$ and $C=\left\{a,d,c\right\}$, then $(A-B)x(B\cap C)$ is equal to

• A. $\left\{(a,c),(a,d)\right\}$
• B. $\left\{(a,b),(c,d)\right\}$
• C. $\left\{(c,a),(d,a)\right\}$
• D. $\left\{(a,c),(a,d),(b,d)\right\}$

Answer 1

The correct option is A

$\left\{(a,c),(a,d)\right\}$

Explanation for the correct option:

Find the value of $\mathbf{(}\mathit{A}\mathbf{}\mathbf{-}\mathbf{}\mathit{B}\mathbf{)}\mathbf{}\mathit{x}\mathbf{}\mathbf{(}\mathit{B}\mathbf{}\mathbf{\cap }\mathbf{}\mathit{C}\mathbf{)}\mathbf{:}$:

Given, $A=\left\{a,b,c\right\},B=\left\{b,c,d\right\}$ and $C=\left\{a,d,c\right\}$,

Now,

$\begin{array}{rcl}A-B& =& \left\{a,b,c\right\}-\left\{b,c,d\right\}\\ & =& \left\{a\right\}\end{array}$

and

$\begin{array}{rcl}B\cap C& =& \left\{b,c,d\right\}\cap \left\{a,d,c\right\}\\ & =& \left\{c,d\right\}\end{array}$

$\begin{array}{rcl}\therefore \left(A-B\right)\times \left(B\cap C\right)& =& \left\{a\right\}\times \left\{c,d\right\}\\ & =& \left\{\left(a,c\right),\left(a,d\right)\right\}\end{array}$

Hence, option ‘A’ is Correct.