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If $A=\{x,y,z\}$ and $B=\{u,v,w,x\}, $ and the universe is $\{s,t,u,v,w,x,y,z\}$. Then $(A \cup \overline{B}) \cap (A \cap B)$ is equal to

  1. $\{u,v,w,x\}$
  2. $\{ \: \}$
  3. $\{u,v,w,x,y,z\}$
  4. $\{u,v,w\}$
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1 Answer

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5 votes
$\bar{B}=\{s,t,u,v,w,x,y,z\}-\{u,v,w,x\} = \{s,t,y,z\}$

$(A\cup\bar{B})=\{s,t,x,y,z\}$

$(A\cap B)=\{x\}$

$(A\cup \bar{B})\cap(A\cap B)=\{s,t,x,y,z\}\cap\{x\}=\{x\}$

But there was no such option.
Answer:

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