In a proof by contradiction, you start by assuming the opposite of what you want to prove. In the case of the statement "If A, then B", the contradiction would be assuming "If A, then not B".

Here are the steps:

1. Assume the statement "If A, then B" is false. This means that even though A is true, B is false. This is our assumption for contradiction, often called the negation of the statement.

2. From this assumption, you would then derive a statement that contradicts either a known fact, or the assumption itself. This could be anything that goes against what we know to be true, or against the assumption we made in step 1.

3. If such a contradiction is found, then the assumption made in step 1 is false. This means that the original statement "If A, then B" is true.

The contradiction in the statement "If A, then B" would be found in step 2, where a statement is derived that contradicts the assumption made in step 1.

Question

In a proof by contradiction, you start by assuming the opposite of what you want to prove. In the case of the statement "If A, then B", the contradiction would be assuming "If A, then not B".

Here are the steps:

1. Assume the statement "If A, then B" is false. This means that even though A is true, B is false. This is our assumption for contradiction, often called the negation of the statement.

2. From this assumption, you would then derive a statement that contradicts either a known fact, or the assumption itself. This could be anything that goes against what we know to be true, or against the assumption we made in step 1.

3. If such a contradiction is found, then the assumption made in step 1 is false. This means that the original statement "If A, then B" is true.

The contradiction in the statement "If A, then B" would be found in step 2, where a statement is derived that contradicts the assumption made in step 1.

Knowee AI · Accepted Answer

In a proof by contradiction, you start by assuming the opposite of what you want to prove. In the case of the statement "If A, then B", the contradiction would be assuming "If A, then not B".

Here are the steps:

1. Assume the statement "If A, then B" is false. This means that even though A is true, B is false. This is our assumption for contradiction, often called the negation of the statement.

2. From this assumption, you would then derive a statement that contradicts either a known fact, or the assumption itself. This could be anything that goes against what we know to be true, or against the assumption we made in step 1.

3. If such a contradiction is found, then the assumption made in step 1 is false. This means that the original statement "If A, then B" is true.

The contradiction in the statement "If A, then B" would be found in step 2, where a statement is derived that contradicts the assumption made in step 1.

what is the contradiction (in proof by contradiction) in the statement "If A, then B"?

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