Question

The set $(A\cup B\cup C)\cap (A\cap B^{\prime }\cap C^{\prime })\cap C^{\prime }$ is equal to

• A. $B\cap C^{\prime }$
• B. $A\cap C$
• C. $B^{\prime }\cap C^{\prime }$
• D. None of these

Answer 1

The correct option is D None of these

Step 1: The venn diagram for $(A\cup B\cup C)$ is

Step 2: The venn diagramm for $(A\cap B^{\prime }\cap C^{\prime })$ is

Step 3: Therefore, venn diagram for $(A\cup B\cup C)\cap (A\cap B^{\prime }\cap C^{\prime })$
Step 4: Venn diagram for $(A\cup B\cup C)\cap (A\cap B^{\prime }\cap C^{\prime })\cap C^{\prime }$ is same as venn diagram of $(A\cup B\cup C)\cap (A\cap B^{\prime }\cap C^{\prime })$