- #1

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## Main Question or Discussion Point

Hi all,

I've got a question about indirect proof, whether I have understood it correctly:

a) Suppose I want to show A=>B, where A and B are two statements.

In the method of indirect proof I assume that [tex]\neg B[/tex] (not B) is true and use the given statement A to show a contradiction. Therefore, B must be true (because either B or [tex]\neg B[/tex] is true).

In short what I do:

[tex]\neg B[/tex] true (assumption) and A true (given statement) => contradiction

Is that correct?

b) Now another question:

Suppose I assume B is true (instead of [tex]\neg B[/tex] true) and use the given statement A such that it leads to a true statement like 1=1.

Have I showed anything with that?

In short what I do here:

B true (assumption) and A true (given statement) => no contradiction.

But that doesn't tell me anything, right?

I've got a question about indirect proof, whether I have understood it correctly:

a) Suppose I want to show A=>B, where A and B are two statements.

In the method of indirect proof I assume that [tex]\neg B[/tex] (not B) is true and use the given statement A to show a contradiction. Therefore, B must be true (because either B or [tex]\neg B[/tex] is true).

In short what I do:

[tex]\neg B[/tex] true (assumption) and A true (given statement) => contradiction

Is that correct?

b) Now another question:

Suppose I assume B is true (instead of [tex]\neg B[/tex] true) and use the given statement A such that it leads to a true statement like 1=1.

Have I showed anything with that?

In short what I do here:

B true (assumption) and A true (given statement) => no contradiction.

But that doesn't tell me anything, right?