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Contrapositive of the statement:

If a function f is differentiable at a , then it is also continuous at a ', is:

Option 1 -

 If a function f is not continuous at a , then it is not differentiable at a .

Option 2 -

If a function f is continuous at a , then it is differentiable at a .

Option 3 -

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

Option 4 -

 If a function f is continuous at a , then it is not differentiable at a .(Reasoning)

0 2 Views | Posted 2 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    2 months ago
    Correct Option - 3


    Detailed Solution:

    ∫03? g (x)-f (x)=∫03? ||x-2|-2|dx-∫03? |x-2|dx

    =12×2×2+1+12×1×1-12×2×2+12×1×1

    =2+1+12-2+12=1

Similar Questions for you

Let Δ∈{∧,∨,⇒,⇔} be such that (p∧q)Δ((p∨q)⇒q) is a tautology. Then Δ is equal to:
A
alok kumar singh

(p∨q)⇒q

= ∼ (p∨q)∨q

=  (∼p∧∼q)∨q

=  (∼p∨q)∧ (∼q∨q)

= ∼p∨q

now  (p∧q)Δ (∼p∨q)is  tautolog? y

pq p∧q ∼p∨q  (p∧q)Δ (∼p∨q)

TTTTT

TFFFT

FTFTT

FFFTT

So,  Δ=  ⇒

Let

p : Ramesh listens to music.

p : Ramesh is out of his village.

r : It is Sunday

s : It is Saturday

Then the statement “Ramesh listens to music only if he is in his village and it is Sunday or Saturday” can be expressed as
V
Vishal Baghel

Let

P : Ramesh listens to music

Q : Ramesh is out of his village

R : It is Sunday

S : It is Saturday

Then the statement “Ramesh listens to music only if he is in his village and it is Sunday or Saturday can be expressed as

P≡ Ramesh listens to music

∼q≡ He is in village.

r∨s≡ Saturday or Sunday

P⇒ ( (∼q)∧ (r∨s))

Given the following two statements:

S1:(q∨p)→(p↔∼q) is a tautology.

S2:∼q∧(∼p↔q) is a fallacy. Then:
A
alok kumar singh

Let TV (r) denotes truth value of a statement r .

 Now, if TV (p)=TV (q)=T

⇒TVS1=F

Also, if TV (p)=T and TV (q)=F

⇒TVS2=T

Which of the following statement is a tautology?
P
Payal Gupta

 ? ( (∼q)∧p)∨ (pv (∼p))

= (∼q∧p)∨t (t  is  )

≡t

∴ option (C) is correct.

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