Question

The contrapositive of "if in a triangle $ABC,AB>AC$, then $\angle C>\angle B$", is

• A. lf in a triangle $ABC,\angle C>\angle B$, then $AB>AC$.
• B. lf in a triangle $ABC,AB\ngtr AC$, then $\angle C\ngtr \angle B$.
• C. lf in a triangle $ABC,\angle C\ngtr \angle B$, then $AB>AC$.
• D. lf in a triangle $ABC,\angle C\ngtr \angle B$, then $AB\ngtr AC$ .

Answer 1

The correct option is D lf in a triangle $ABC,\angle C\ngtr \angle B$, then $AB\ngtr AC$ .

Take $p:AB>AC$

and $q:\angle C>\angle B$

So the given statement is symbolically represented as $p\to q$

Now by definition, Contrapositive of a conditional statement $p\to q$ is $\sim q\to \sim p$

$\sim p:AB\ngtr AC$

$\sim q:\angle C\ngtr \angle B$

Thus $\sim q\to \sim p$ is given by

"If in a $△ABC,\angle C\ngtr \angle B$ then $AB\ngtr AC$."