Question

If $E$ is the universal set and $A=B\cup C$, then the set $E-(E-(E-(E-(E-A\left)\right)\left)\right)$ is same as the set

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

Answer 1

Answer: (C)

$B^{\prime }\cap C^{\prime }$

$E–(E–(E–(E–(E–A\left)\right)\left)\right)=E–(E–(E–(E–A^{\prime })\left)\right)=E–(E–(E–A\left)\right)=E–(E–A^{\prime })=E–A=A^{\prime }$

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

Hence, the answer is $B^{\prime }\cap C^{\prime }$