Question

If $A,B$ and $C$ are three finite sets, then what is $\left[\right(A\cup B)\cap C]\text{'}$equal to?

• A. $A\text{'}\cup B\text{'}\cap C\text{'}$
• B. $A\text{'}\cap B\text{'}\cap C\text{'}$
• C. $A\text{'}\cap B\text{'}\cup C\text{'}$
• D. $A\cap B\cap C$

Answer 1

The correct option is C

$A\text{'}\cap B\text{'}\cup C\text{'}$

Find the value of $\mathbf{\left[}\mathbf{\right(}\mathit{A}\mathbf{\cup }\mathit{B}\mathbf{)}\mathbf{}\mathbf{\cap }\mathit{C}\mathbf{]}\mathbf{\text{'}}$:

Given that $A,B$ and $C$ are three finite sets

$\left[\right(A\cup B)\cap C]\text{'}=(A\cup B)\text{'}\cup C\text{'}$

$$\begin{gathered} =(A\text{'}\cap B\text{'})\cup C\text{'} \\ =A\text{'}\cap B\text{'}\cup C\text{'} \end{gathered}$$

Hence, the correct option is (C).