Question

Which of the follwing is correct?

• A. $A$ intersection $\phi =A$
• B. $A$ intersection $\phi =\varphi$
• C. $A$ intersection $\phi =U$
• D. $A$ intersection $\phi =A\text{'}$

Answer 1

The correct option is B

$A$ intersection $\phi =\varphi$

Determining the correct option.

Here, $\varphi$ denotes an empty set.

If any set is in intersection with an empty set then there will be nothing common between them and the result eventually will be an empty set itself.

Therefore,

$A\cap \varphi =\varphi$

The intersection of any set with an empty set, is an empty set.

Hence, the correct answer is Option (B).