Contrapositive of the statement:

Question:

Contrapositive of the statement:

'If a function $\mathrm{f}$ is differentiable at a, then it is also continuous at a', is :-

 

  1. If a function $\mathrm{f}$ is continuous at $\mathrm{a}$, then it is not differentiable at a.

  2. If a function $\mathrm{f}$ is not continuous at $\mathrm{a}$, then it is differentiable at a.

  3. If a function $\mathrm{f}$ is not continuous at a, then it is not differentiable at a.

  4. If a function $\mathrm{f}$ is continuous at $\mathrm{a}$, then it is differentiable at a.

Correct Option: , 3

Solution:

$\mathrm{p}=$ function is differantiable at a

$\mathrm{q}=$ function is continuous at a

contrapositive of statement $\mathrm{p} \rightarrow \mathrm{q}$ is

$\sim \mathrm{q} \rightarrow \sim \mathrm{p}$

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