Match the following: item 1. Indirect proof which assumes the opposite of a stat

Question

Match the following: item 1. Indirect proof which assumes the opposite of a statement and shows this creates a logical inconsistency item 2, Indirect proof applied to a statement of the form PQ which instead proves-Q-P. item 3. Proves a "there exists" statement by finding a specific element for which the statement is true item 4. Disproves a "for all" statement by finding a specific element for which the statement is false. item 5. Proof where a statement is split into multiple sub-statements, and each of these sub-statements is proven. choice a. Proof by Counter-Example choice b. Proof by Contraposition choice C. Proof by Cases choice d. Proof by Example (Existence Proof) choice e. Proof by Contradiction

Explanation / Answer

Item 1 This is a proof by contradiction

Item 2 This corresponds to a proof by contraposition

Item 3 corresponds to proof by example as an example is given where the statement holds

Item 4 corresponds to proof by a counter example as it gives an instance for which the statement is not true

Item 5 corresponds to proof by cases where we prove each case

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