I'm struggling a bit with these formulas, whether they are tautologies or not; 1) 2) Any help/tips on where to start/solve these would be greatly appreciated!
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Hmmm....
Originally Posted by jokke22 2) A. B. Suppose that reads “x is causes y”. Then the A statements reads: Something is caused by everything. The B statement reads: Everything causes something. Now does A imply B?
Originally Posted by jokke22 2) 1. 2. (by deduction theorem) 3. (by rule EI, existential instantiation) 4. (by generalization theorem) 5. (by generalization theorem) 6. (contraposition) 7. (quantifier axiom) Thus, (2) is tautology.
Originally Posted by aliceinwonderland 1. 2. (by deduction theorem) 3. (by rule EI, existential instantiation) 4. (by generalization theorem) 5. (by generalization theorem) 6. (contraposition) 7. (quantifier axiom) Thus, (2) is tautology. That is thorough! Thank you! Those rules any site which shows "all" used in predicate logic? My school book is missing out on some of them. As for A), struggling hard myself, any help/suggestion on this as well?
Originally Posted by jokke22 1) 1. . 2. . 3. . 4. . 5. . Note. Since is not valid, 5 is not valid. 3 uses the rule of union for existential quantifier (link).
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