mt1-s00

mt1-s00 - CS 70 Spring 2000 Discrete Mathematics for CS...

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CS 70 Discrete Mathematics for CS Spring 2000 Wagner Midterm 1 You have 1 hour and 20 minutes. The exam is open-book, open-notes. 100 points total (five questions of varying credit as shown). You should be able to finish all the questions, so avoid spending too long on any one question. . Write your answers in blue books. Check you haven’t skipped any by accident. Hand them all in. Panic not. 1. (20 pts.) Satisfiability and all that For each of the following Boolean expressions, decide if it is (i) valid (ii) satisfiable (iii) unsatisfiable. (Give all applicable properties, with justifications.) (a) (5) A ∧¬ A ∧¬ B (b) (10) ( A = B ) ( B = C ) ( C = ⇒ ¬ A ) (c) (5) ( A = B ) ( B = A ) 2. (25 pts.) Induction Given a binary tree t , the depth depth ( l , t ) of a leaf l in t is defined to be the length of the path from l to the root of t . (Hence, if t is just an atom l , then depth ( l , t ) = 0.) (a) (3) In the tree t below, what are the depths of the 3 leaves
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mt1-s00 - CS 70 Spring 2000 Discrete Mathematics for CS...

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