Question

Using DeMorgan's law, which of the following is equivalent to the statement $C\cap (B\cup A\text{'}){}^{\prime }$ ?

• A. $C\cap (B{}^{\prime }\cup A){}^{\prime }$
• B. $C{}^{\prime }\cap (B{}^{\prime }\cup A{}^{\prime })$
• C. $(C\cup B)\cap A{}^{\prime }$
• D. $C\cap (B{}^{\prime }\cap A)$

Answer 1

The correct option is D $C\cap (B{}^{\prime }\cap A)$

The given set is $C\cap (B\cup A\text{'}){}^{\prime }$

So, taking two sets $A$ and $B$ into consideration for Demorgan laws

Now, using Demorgan law of union of set $A$ and $B$,

$(B\cup A{}^{\prime }){}^{\prime }$ = $(B{}^{\prime }\cap A{}^{\prime }{}^{\prime })$ = $(B{}^{\prime }\cap A)$

Now, taking intersection of set $(B{}^{\prime }\cap A)$ with set $C$, we get,

$C\cap (B{}^{\prime }\cap A)$