Question

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

Answer 1

@wolfe8

Answer 2

@robtobey

Answer 3

I know how to do it but I don't know how to explain it

Answer 4

Sorry I don't know this :/ Good luck

Answer 5

Indirect proofs say the opposite. Assume what you need to prove is false, and then show that something contradictory (absurd) happens.

Stephen broke his brother's Xbox last night.

Stephen did not break his brother's Xbox last night.
Stephen was not home last night.
Stephen couldn't have broken his brother's Xbox.

By proving something contradictory to the initial argument (e.g., that Stephen broke his brother' Xbox) you have proved, indirectly, that he couldn't have possibly broken it.


Follow these Steps!:

Assume that the opposite of what you are trying to prove is true.
From this assumption, see what conclusions can be drawn. These conclusions must be based upon the assumption and the use of valid statements.
Search for a conclusion that you know is false because it contradicts given or known information. Oftentimes you will be contradicting a piece of GIVEN information.
Since your assumption leads to a false conclusion, the assumption must be false.
If the assumption (which is the opposite of what you are trying to prove) is false, then you will know that what you are trying to prove must be true.
__________________________________________________________________


If I were to say "A triangle is 180 degrees."

I could say:

A triangle is 180 NOT 180 degrees."
Each angle of a triangle measure 90 degrees.
A triangle has three angles.

We can assume, that from this proof, indirectly, that a triangle MUST be 180 degrees, because we contradicted our original statement.

I could also say: Triangle ABC is NOT an isosceles triangle

Proof:
1. Triangle ABC is an isosceles triangle
2. A is the vertex.
3. Angle B and D are not congruent
4. AB and AD are congruent
5. Angles B and D are congruent

Contradiction (3, and 5)

We know that, if angle AB and AD are congruent, than their respective angles must be congruent, too. So, we proved this, by proving other statements. This is also an indirect proof. Basically, an indirect proof is proving something by proving others things. Just like how Stephen broke the Xbox, we proved that he was not home, so that contradicts his brother's statement, so he could NOT have possibly broke the Xbox.



Regards,



OpenStudy Ambassador, OpenStudy Team.

Answer 6

Thank you so much! That made a lot of sense!