whats a contradictory statement of "all men are honest,".

Question

anonymous · Answer

all men are dishonest

apoorvk · Answer

"All men are not honest".

basically if a statement is given that is valid for all cases, the contradictory statement for it would one where the theory in the statement is that the rule is violated for ATLEAST for case.

So, if p=All men are honest.
~p=Not all men are honest. -OR- All men are not honest

anonymous · Answer

thanks that what i got you guys!!!!!

apoorvk · Answer

@kevinkeegan are you sure? I am doubtful about what you say.

anonymous · Answer

lol whatever

apoorvk · Answer

There is a difference between "all men are dishonest' and "not all men are honest". The later means that "tere is ATLEAST one dishonest person". the former means that "all are dishonest"

apoorvk · Answer

*there

anonymous · Answer

so could it also be some men are dishonest?

lgbasallote · Answer

your teacher is a woman isnt she =_=

apoorvk · Answer

LOLLL!!

apoorvk · Answer

Nope not 'some' - I know that there all aren't honest. We don't know how many - 1, 2, 3, 100, or everyone's dishonest - no we don't know that - but not all are honest - 'there exists atleast one man who is not honest" - this is also a valid contradiction.

blockcolder · Answer

$$p(x) - \text{A person is a man.}\
q(x) - \text{A person is dishonest.}\
\text{All men are dishonest} \equiv \forall x(p(x) \to q(x))\
\text{Negation is} \exists x(p(x) \wedge \neg q(x))$$
Therefore, a contradicting statement is "At least one man is not dishonest (honest)."