PROOF By CONTRADICTION .

recently i was doing some prove problems where there was a question which was to be proved by the indirect proof method. But i am a little puzzled about when to use the indirect proof method. Could anyone help over that plzzzz!!!

#ProofTechniques #Proofs #FalseProofs

Easy Math Editor

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`2 \times 3`	$2 \times 3$
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`\frac{2}{3}`	$\frac{2}{3}$
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Comments

@Palash Som Check out this wiki by Mursalin Habib

U Z - 6 years, 5 months ago

ya thats a great one , but it do not provide the condition when we can use the indirect proof . i was doing a problem of circles which was done by contradiction . the question asked " prove that the perpendicular bisectors of 2 chords in a circle C(O,r) meet at the center of that circle " So here they just assume to take the point of intersection of the perpendicular bisectors away from the center and then they proved it by contradiction . So i am just asking for some special cases where one could always apply the contradiction . @megh choksi

Palash Som - 6 years, 5 months ago

Theorem says The perpendicular from the center of a circle to a chord bisects the chord. And contradiction can be used if we have sufficient conditions to contradict means depend's upon the problem.

shivamani patil - 6 years, 5 months ago

@Shivamani Patil – check RD sharma its one of the corollary

Palash Som - 6 years, 5 months ago

I think I understand what you're trying to say.

There's no such thing as a "list of all problems that require proof by contradiction". So, you can't look at a problem and immediately go, "Hey, I know! I'm going to use contradiction here."

Sometimes you have to ask yourself, "Does negating the conclusion help me in some way? Does it give me something easier to work with?" If the answers are 'yes', you should definitely try a contradiction argument.

Being able to determine what approach will work for a certain problem also comes with experience. When you first learn about a topic, say induction, you don't immediately know if a certain problem can be approached using induction. As you learn and become more experienced, you develop some sort of intuition that allows you to say, "Hey, I think if I do this and this, an induction proof might work."

Also check out the heading titled "motivation" in the same wiki for more details.

Mursalin Habib - 6 years, 5 months ago

@Mursalin Habib – i understood what you 're saying thnx !

Palash Som - 6 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$