MAT-2510 Midterm: MATH 2510 App State Spring2015 Test1 answer key
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Answer key: (10 points) consider theorem l15: a (a b) (a) show l15 is a tautology using by lling out an abbreviated truth table. T (b) prove l15 in system l. [you may use the deduction theorem and theorems l1 l14. ] Hint: i have a quick proof using the deduction theorem and lemmas l5 and l10 in mind. We know that the theorems of l (the statements provable in l) are exactly the tautologies. In particular, the soundness theorem for system l says that only tautologies can be proven in l. the completeness theorem for system l says that every tautology can be proven in l. hence, to determine whether a b . A and a a b are provable in l we simply need to check to see if each statement is a tautology. Recall that c d is equivalent to c d. (a b) a.
