question_answer

Let U be the universal set and \[A\cup B\cup C=U\]. Then \[[(A-B)\cup (B-C)\cup (C-A)]'\]equals

A) \[A\cup B\cup C\]                      

B) \[A\cap B\cap C\]

C) \[A\cup (B\cap C)\]                    

D) \[A\cap (B\cup C)\]

Correct Answer: B

Solution :

[b]            \[A-B\to \text{ }Regions\,\,3\,\,and\,\,5.\] \[B-C\to \text{ }Regions\,\,5\,\,and\,\,6.\] \[C-A\to \text{ }Regions\,\,4\,\,and\,\,7\] \[\therefore (A-B)\cup (B-C)\cup (C-A)\to Regions\,\,2,3,4,5,6,7\] \[\therefore {{[(A-B)\cup (B-C)\cup (C-A)]}^{\prime }}\to Region\,\,1,\] \[which\,\,is\text{ }A\cap B\cap C\]