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6 Cards in this Set
- Front
- Back
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Law of Contrapositive
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if the conditional is true, then the contrapositive is true
PROOF- (p ⟶ q) ⟷ (∼q ⟶ ∼p) |
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DeMorgan's Law
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two laws, one stating that the denial of the conjunction of a class of propositions is equivalent to the disjunction of the denials of a proposition, and the other stating that the denial of the disjunction of a class of propositions is equivalent to the conjunction of the denials of the propositions.
PROOF- ∼(p ⋀ q) ⟷ (∼p ⋁ ∼q) |
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Law of Conjunctive Simplification
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p ⋀ q
∴q ∴p PROOF- No proof |
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Law of Disjunctive Inference
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p ⋁ q
∼p ∴q PROOF- [( p ⋁ q) ⋀ ∼p] ⟶ q |
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Law of Detachment
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- hypothesis ⟶ conclusion
p ⟶ q p ∴q PROOF- [(p ⟶ q) ⋀ p] ⟶ q |
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Tautology
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An empty or vacuous statement composed of simpler statements in a fashion that makes it logically true whether the simpler statements are factually true or false; when all outcomes on a Truth table are true
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