question_answer

If A and B are two sets then \[\left( A\text{ }-\text{ }B \right)\text{ }\cup \text{ }\left( B\text{ }-\text{ }A \right)\text{ }\cup \text{ }\left( A\text{ }\cap \text{ }B \right)\] is equal to

A) \[A\text{ }\cup \text{ }B\]

B) \[A\text{ }\cap \text{ }B\]

C) A

D) \[{B}'\]

Correct Answer: A

Solution :

From Venn-Euler's diagram, \[\therefore \] \[(A-B)\,\cup (B-A)\cup (A\cap B)=A\cup B\].