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MIT6_042JF10_mid_practice - 6.042/18.062J Mathematics for...

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6.042/18.062J Mathematics for Computer Science October 21, 2010 Tom Leighton, Marten van Dijk, and Brooke Cowan Midterm Practice Problems Name: This quiz is closed book , but you may have one 8 . 5 × 11” sheet with notes in your own handwriting on both sides. Calculators are not allowed. You may assume all of the results presented in class. Please show your work. Partial credit cannot be given for a wrong answer if your work isn’t shown. Write your solutions in the space provided. If you need more space, write on the back of the sheet containing the problem. Please keep your entire answer to a problem on that problem’s page. Be neat and write legibly. You will be graded not only on the correctness of your answers, but also on the clarity with which you express them. If you get stuck on a problem, move on to others. The problems are not arranged in order of difficulty.
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2 Midterm Practice Problems Problem 1. [10 points] In problem set 1 you showed that the nand operator by itself can be used to write equivalent expressions for all other Boolean logical operators. We call such an operator universal . Another universal operator is nor , defined such that P nor Q ( P Q ). ⇔ ¬ Show how to express P Q in terms of: nor , P , Q , and grouping parentheses.
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MIT6_042JF10_mid_practice - 6.042/18.062J Mathematics for...

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