JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Mathematical Reasoning *

Contrapositive of the statement:
'If a function f is differentiable at a, then it is also continuous at a', is:

(A)If a function f is not continuous at a, then it is not differentiable at a.✓ Correct
(B)If a function f is continuous at a, then it is differentiable at a.
(C)If a function f is not continuous at a, then it is differentiable at a.
(D)If a function f is continuous at a, then it is not differentiable at a.

Answer: (A)

Solution

The contrapositive of

p \Rightarrow q

\sim q \Rightarrow\sim p

. Taking

p

as "

f

is differentiable at

a

" and

q

as "

f

is continuous at

a

", the contrapositive reads: if a function

f

is not continuous at

a

, then it is not differentiable at

a

JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Single correct option