Indirect Proof

Front

What is an indirect proof?

Back

An indirect proof is a method of proving a statement by assuming the opposite of what you want to prove and showing that this assumption leads to a contradiction.

Front

What is the first step in an indirect proof?

Back

The first step is to assume the negation of what you are trying to prove.

Front

What is the second step in an indirect proof?

Back

The second step is to contradict the given using logical statements based on the initial assumption.

Front

What assumption would you make to start the indirect proof of if 3x+7>13, then x>2?

Back

You would assume x≤2.

Front

What assumption would you make to start the indirect proof of AB≅BC?

Back

You would assume AB≠BC.

Front

In an indirect proof, what does it mean to reach a contradiction?

Back

Reaching a contradiction means that the assumption made at the beginning must be false, thus proving the original statement true.

Front

What is the purpose of assuming the negation in an indirect proof?

Back

The purpose is to explore the consequences of the assumption and demonstrate that it leads to an impossible situation.

Front

What is a temporary assumption in an indirect proof?

Back

A temporary assumption is an assumption made to explore the validity of a statement, which is later shown to be false.

Front

What is the conclusion of an indirect proof?

Back

The conclusion is that the original statement is true because the assumption made leads to a contradiction.

Front

What is the relationship between indirect proof and logical reasoning?

Back

Indirect proof relies on logical reasoning to show that an assumption leads to a contradiction, thereby validating the original statement.