Question

If A, B and C are any three sets, then $A-(B\cup C)$ is equal to

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

Answer 1

The correct option is B $(A-B)\cap (A-C)$

$U-(P\cup Q)=(P\cup Q{)}^c$
$(P\cup Q{)}^c=P^c\cap Q^c=(U-P)\cap (U-Q)$
It is De' Morgan law.

Now, just replace U with A, P with B and Q with C.
We will get,
$A-(B\cup C)=(A-B)\cap (A-C)$