Question

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

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

Answer 1

Answer: (C)

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

Given, A, B and C are three finite sets, then

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

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