HW5-SOLUTIONS - Homework 5 Solutions Thanks to Sean Lavelle...

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Sheet1 Page 1 Homework 5 Solutions Thanks to Sean Lavelle for providing these solutions. Skip to #: 1 - 2 - 3 - 4 - 5 - 6 - 7 import Stdm impSelf = thmEq (Imp A A) TRUE {- Problem 1 -} --deMorgansLawAnd: (not(a and b)) = ((not a) or (not b)) thm1 = (Not(A `And` B)) `thmEq` ((Not A) `Or` (Not B)) prf1 = startProof (Not(A `And` B)) <-> (Not((Not(Not A)) `And` B), dblNeg) <-> (Not((Not(Not A)) `And` (Not(Not B))), dblNeg) <-> (Not(Not((Not A) `Or` (Not B))), deMorgansLawOr) <-> ((Not A) `Or` (Not B), dblNeg) {------------------------------------------------------------------------------------------------} {- Problem 2 -} --exclMiddle: (a or (not a)) = True thm2 = (A `Or` (Not A)) `thmEq` TRUE prf2 = startProof (A `Or` (Not A)) <-> ((Not A) `Or` A, orComm) <-> (A `Imp` A, implication) <-> (TRUE, impSelf) {------------------------------------------------------------------------------------------------} {- Problem 3 -} --negT: (not True) = False thm3 = (Not TRUE) `thmEq` FALSE prf3 = startProof(Not TRUE)
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HW5-SOLUTIONS - Homework 5 Solutions Thanks to Sean Lavelle...

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