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#1
what do the terms "proof by contradiction" and "disproof by counter-example" mean and has anyone gt any examples i can try ??

#C3 maths
0
4 years ago
#2
disproof by counter example is as simple as giving a mn example which does not satisfy the statement made.

Not too sure on propf by contradiction
0
4 years ago
#3
Proof of contradiction involves assuming that what you are trying to disprove is actually true. Then you show that the consequences of this contradict logic.
For example, you can use contradiction to prove that the square root of 2 is irrational.

Assume that the square root of 2 is rational. Then it can be expressed as p/q, where p and q are integers. Let p and q be co-prime, otherwise divide by their common factors.
So 2 = p/q squared. Rearrange this into p^2 = 2q^2. Therefore p^2, and p, divides by 2.
Because p divides by two, we can let p = 2r, where r is an integer.
Therefore 4r^2 = 2q^2, or 2r^2 = q^2. Therefore q divides by 2.

So p and q divide by two. But we said that they shared no common factors in the beginning! This is a contradiction, so the square root of 2 cannot be rational. QED.
1
4 years ago
#4
(Original post by Virolite)
what do the terms "proof by contradiction" and "disproof by counter-example" mean and has anyone gt any examples i can try ??

#C3 maths
Proof by contradiction - you're given a statement to prove. Begin by assuming that the complete opposite of the statement is true, and work your way to some contradiction.

Proof by counter-example - you're given a statement to prove, alongside some conditions that should be given/obvious. All you need to do is find an example satisfying the conditions but not the statement.
0
4 years ago
#5
Contradiction - prove the opposite of the statement is true.
Disproof by counter-example is like exhaustion except you're proof is that you can't exhaust the solutions because the one you use does not work for the proof
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