contradiction

Question

By which of the following proposition, the proposition ‘wise men are hardly afraid of death’ is contradicted ?

(A) Some wise men are afraid of death.

(B) All wise men are afraid of death.

(C) No wise men is afraid of death.

(D) Some wise men are not afraid of death.

Answer 1

this means there are some wise men who is  not afraid of death..

Let w(x) : x is a wise men

A(x) : x is afraid of death

Therefore we get ∃x( w(x)∧∼A(x) )

Now if we negate it we get...

∼∃x( w(x)∧∼A(x) )

∀x(∼w(x) ∨ A(x))

∀x( w(x)→A(x))

this means all wise men are afraid of death

which is option B

Comments

how u know some wise man it can be all wise man also

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they have told wise men are hardly afraid of death...means some wise men are afraid of death.....(whose proportion is less)..and some wise men are not afraid of death

Answer 2

Ans (D) Some wise men are not afraid of death.

i.e. not all wise men are not afraid of death.

Contradiction happen when truth value is always false

Comments

They have told hardly which means some wise men are afraid of death.....some wise men are not afraid of death....but the possibility of former is rare by still there can be some wise men who is afraid of death...if we negate the former we get all wise men are not afraid of death..which is not in option....so I have taken the later one whose negation is option b

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A and D can surely  be not the ans as draw a venn diagram in which have a small fraction of common area between two circular regions one representing wise men another afraid of death .  so it naturally implies some wise men are not afraid of death and some are afraid of death so A,D choice are out .confusion can only be in B and C

Answer 3

hardly means " almost not" or "not at all" or "barely".. so meaninig of this sentence looks like " wise men are almost not afraid of death."means "a very few wise men(almost no one) who is afraid of death." so contradiction of this staement should be " all wise men are afraid of death." option B

Answer 4

@Sanjay. By ‘wise men are hardly afraid of death’ , we mean there is hardly anyone who is afraid of death or the proportion is so less that it can be ignored. It means (as I think),

Vx(   W(x)  -> --A(x)   )

Now, negation is    (there exists X) (    W(x)   ^    A(x)   ).

Previously, I could hardly point out anyone who is afraid of death. Now, there exists a wise person which I can point out who is afraid of death.

SO, answer is (A).