Question

write the converse, inverse and contrapositive,
If a function is differentiable then it is continuous.​

Answer 1

Topic :-

Mathematical Reasoning

Given :-

If a function is differentiable then it is continuous.

To Find :-

Converse, Inverse and contrapositive of given conditional statement.

Solution :-

Let,

p = A function is differentiable.

q = It is continuous.

Given : p → q

Converse

The converse of the conditional statement p → q is defined as q → p.

Converse of given statement,

If a function is continuous then it is differentiable.

Inverse

The inverse of the conditional statement p → q is defined as ~p → ~q

Inverse of given statement,

If a function is not differentiable then it is not continuous.

Contrapositive

The contrapositive of conditional statement p → q is defined as ~q → ~p.

Contrapositive of given statement,

If a function is not continuous then it is not differentiable.