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HW4 - CS 2603 Applied Logic for Hardware and Software...

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Sheet1 Page 1 CS 2603 Applied Logic for Hardware and Software Homework 4 Due Tuesday, Feb 12, 2:59pm, in the classroom Late Homework not accepted FAQ Warning! These are hard problems. And, you must solve them if you want to pass exams. Expect to spend a lot of time on this homework. Problems 1 - 4: Prove using the inference rules of natural deduction (not the equations/laws of Boolean algebra). 1. A -> B |- (Not A) \/ B [note: "implication, forward direction" is a name for this theorem] 2. A -> B, A -> (Not B) |- Not A (use proof checker on this one) [note: "absurdity, forward direction" is a name for this theo 3. Not A |- (A -> B) /\ (A -> (Not B)) [note: "absurdity, backward direction" is a name for this theorem] 4. A \/ (B \/ C) |- (A \/ B) \/ C (use proof checker on this one) [note: "\/ associative, forward direction" is a name for this th Note: You may use cite previously-proved theorems as reasons for steps in the proof, including theorems from the lectures, a Problems 5 - 8: Prove using equational reasoning (that is, the equations/laws of Boolean algebra). In addition, for problem 6, d 5. (A \/ B) /\ B = B
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