Question

State whether each of the following statements is true or false.

If the statement is false rewrite the given statement correctly.

If $A=\{1,2\},B=\{3,4\}$ then $A\times (B\cap \varphi )=\varphi$

• A. True
• B. False

Answer 1

The correct option is A True

Explanation.

The given set is, $A=\{1,2\},B=\{3,4\}$.

Consider the LHS of the given expression,

$$\begin{gathered} \mathrm{LHS}=A\times (B\cap \varphi ) \\ =A\times \varphi \left[\because B\cap \varphi =\varphi \right] \\ =\varphi \\ =\mathrm{RHS} \end{gathered}$$

Hence, the given statement is true.