Question

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

• A. $A\cap (B\cup C)$
• B. $A\cup (B\cap C)$
• C. $A\times (B\cup C)$
• D. $A\times (B\cap C)$

Answer 1

The correct option is C

$A\times (B\cup C)$

Explanation for the correct option:

Finding the value of $\mathbf{\left\{}\mathbf{\right(}\mathit{a}\mathbf{,}\mathit{c}\mathbf{)}\mathbf{,}\mathbf{(}\mathit{a}\mathbf{,}\mathit{d}\mathbf{)}\mathbf{,}\mathbf{(}\mathit{a}\mathbf{,}\mathit{e}\mathbf{)}\mathbf{,}\mathbf{(}\mathit{b}\mathbf{,}\mathit{c}\mathbf{)}\mathbf{,}\mathbf{(}\mathit{b}\mathbf{,}\mathit{d}\mathbf{)}\mathbf{,}\mathbf{(}\mathit{b}\mathbf{,}\mathit{e}\mathbf{\left)}\mathbf{\right\}}\mathbf{:}$

Given, $A=\{a,b\},B=\{c,d\},C=\{d,e\}$

$(B\cup C)=\{c,d,e\}$

$(B\cap C)=\left\{d\right\}$

Now, $A\cap (B\cup C)=\varphi$

$A\cup (B\cup C)=\left\{a,b,c,d,e\right\}$

$\mathbf{\therefore }\mathit{A}\mathbf{\times }\mathbf{(}\mathit{B}\mathbf{\cup }\mathit{C}\mathbf{)}\mathbf{=}\left\{(a,c),(a,d),(a,e),(b,c),(b,d),(b,e)\right\}$

Hence, The correct option is (C)