Math

QuestionWhat is the term for a proof that assumes the opposite of the conclusion? A. Proof by contradiction B. Proof by syllogism C. Proof by contrapositive D. Proof by inverse

Studdy Solution

STEP 1

Assumptions1. We are looking for a term that describes a proof method where we assume the opposite of what we want to prove.

STEP 2

Consider each of the given options and compare them with the description provided in the problem.

STEP 3

Option A Proof by contradiction. In this method, we assume the opposite of what we want to prove and show that this leads to a contradiction, thus proving our original statement.

STEP 4

Option B Proof by syllogism. This is a form of logical argument where a conclusion is drawn from two given or assumed propositions.

STEP 5

Option C Proof by contrapositive. In this method, we prove a statement by showing that the denial of the conclusion implies the denial of the hypothesis.

STEP 6

Option D Proof by inverse. This method involves proving a statement by showing that the inverse of the statement is true.

STEP 7

Compare the description given in the problem with each of the options. The description matches with the method of Proof by contradiction.
The term that best describes a proof in which you assume the opposite of what you want to prove is Proof by contradiction.

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