There are two kinds of indirect proofs: the proof by contrapositive, and the proof by contradiction. $\Z_n$ 3. Note the not .

Notice that both you and Rachel came to the same conclusion, but you got to that concl… The Euclidean Algorithm 4. With an indirect proof, instead of proving that something must be true, you prove it indirectly by showing that it cannot be false.

The proof by contrapositive is based on the fact that an implication is equivalent to its contrapositive. Then n = 2k for some Suppose that the conclusion is false, i.e., that n is even. Rachel looks at you and says, ''If the art festival was today, there would be hundreds of people here, so it can't be today.'' To prove that \(p \Rightarrow q\), we proceed as follows: Suppose \(p\Rightarrow q\) is false; that is, assume that \(p\) is true and \(q\) is false. The GCD and the LCM 7. Therefore, instead of proving p \Rightarrow q, we may prove its contrapositive \overline {q} \Rightarrow \overline {p}. Discrete Math Basic Proof Methods 1.6 Introduction to Proofs Indirect Proof Example Theorem (For all integers n) If 3n+2 is odd, then n is odd. Proof.

Proof by Contradiction Another indirect proof is proof by contradiction. You take out your tickets, look at the date and say, ''The date on the tickets is for tomorrow, so the art festival is not today.'' Argue until we ¥Use logical reasoning to deduce a sequence of facts.

Indirect Proof 3 Number Theory 1.

Indirect Proofs ¥Instead of starting with the given/known facts, we start by assuming the opposite of what we seek to prove.

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