In an indirect proof, we assume that the fact we wish to prove is actually Blank 1 Question 29 .

In an indirect proof, we assume that the fact we wish to prove is actually false. This method of proving a statement can be quite effective, especially in mathematical and logical contexts. To carry out an indirect proof, the assumption that the proposition is false is made, and then through logical reasoning and deduction, a contradiction arises.

This contradiction indicates that the original assumption must be incorrect, thereby affirming that the statement we initially set out to prove is indeed true. The process highlights the fundamental principle of logical implications: if assuming the opposite of what we intend to prove leads to an impossibility or inconsistency, we can conclude that our original statement holds true.

Indirect proofs are particularly useful in scenarios where direct proof may be cumbersome or difficult to construct. By starting with the assumption that contradicts the statement, one can often uncover relationships and properties that directly support the truth of the desired conclusion.