Question

Negation of the statement "If $△ABC$ is isosceles then the base angle's $A$ and $B$ are equal" , is

• A. $△ABC$ is isosceles and the base angles $A$ and $B$ are not equal.
• B. $△ABC$ is not isosceles and the base angles $A$ and $B$ are not equal.
• C. $△ABC$ is not isosceles and the base angles $A$ and $B$ are equal.
• D. $△ABC$ is not isosceles or the base angles $A$ and $B$ are not equal.

Answer 1

The correct option is A $△ABC$ is isosceles and the base angles $A$ and $B$ are not equal.

Let, $p:$ $△ABC$ is isosceles
$q:$ the base angle $A$ and $B$ are equal

We know that, $\sim (p\Rightarrow q)=p\wedge \sim q$

Hence, negation of the given statement is:
$△ABC$ is isosceles and the base angles $A$ and $B$ are not equal.