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Lecture-09

# Lecture-09 - Lecture 9 Conditional Proof Nested Subproofs...

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1. Conditional Proof 2. Examples 3. Nested Subproofs 4. Examples 6. Examples 5. Tautologies Lecture 9 Conditional Proof, Nested Subproofs, & Tautologies Second of two ‘proof strategies’ Conditional Proof Basic idea: prove the conditional ! ! is true, by assuming ! and deriving ! . At some point in a proof, you decide you’d like to be able to derive ! ! on a line, but you can’t figure out how. Add an assumption line consisting of ! , then proceed using the rules. Conditional Proof Keep deriving lines until you derive ! . At this point, we don’t know whether ! is actually true, since we just assumed it, but we have shown that if ! were true, then ! would be true. Conditional Proof But this fact that the subproof demonstrated, that if ! is true, then ! is true, just is what the conditional ! ! means. So the subproof shows that the conditional can be validly infered. Conditional Proof Rules for the use of CP 2. CP ends any time you want 1. Start subproof (SP) by indenting and designating first line ACP 3. Mark off CP, closing SP and

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