JEE Main & Advanced
Mathematics
Sets
Question Bank
Set theory
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,
\[\therefore \] \[(A-B)\,\cup (B-A)\cup (A\cap B)=A\cup B\].