Question

How do you use methods of an indirect proof to determine whether a short proof is logically valid?

Answer 1

do you have an example

Answer 2

you can use proof by contradiction

assume the negation of your claim , show that this leads to a contradiction.
so your claim must be true.

Answer 3

well not really but the lesson is on indirect proofs

Answer 4

for example :
Claim: sqrt(2) is irrational
proof : assume sqrt(2) is rational (negation of the original claim)
we can show that a contradiction follows if sqrt(2) = p/q

Answer 5

can you give me another example ?

Answer 6

lets do an easier proof. since that one is kind of hard

claim : if n is even then n^2 is even.

Answer 7

Indirect Proof:
Assume what you need to prove is false, and then show that something contradictory (absurd) happens.

Answer 8

http://www.regentsprep.org/Regents/math/geometry/GP3b/indirectlesson.htm

Answer 9

ok thanks a lot

Answer 10

yes ?

Answer 11

ok so assume the claim above is false.
ie, it is false that ' if n is even then n^2 is even'. This is a little harder to negate than the last example. How do you negate a conditional?
Negating p->q is p and not q.
This means that n is even and n^2 is not even (odd).
From this can we produce a contradiction?

Answer 12

cant you say if n^2 is odd then n has to be even ?

Answer 13

well we are given that n is even and n^2 is odd by negating our original statement.
actually if n^2 is odd then n is odd. but that is harder to prove.
how about this, if n is even, then n = 2k, then n^2 = 4k^2, so n^2 is even. but we assumed that n^2 is odd. contradiction

Answer 14

ok give me a moment

Answer 15

i honestly dont have a clue