MIT6_042JS10_lec06_prob

# MIT6_042JS10_lec06_prob - Massachusetts Institute of...

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Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science February 17 Prof. Albert R. Meyer revised February 11, 2010, 1155 minutes In-Class Problems Week 3, Wed. Problem 1. For each of the logical formulas, indicate whether or not it is true when the domain of discourse is N (the nonnegative integers 0, 1, 2, . . . ), Z (the integers), Q (the rationals), R (the real numbers), and C (the complex numbers). x ( x 2 = 2) x y ( x 2 = y ) y x ( x 2 = y ) = 0 ( xy = 1) x y x y ( x + 2 y = 2) (2 x + 4 y = 5) Problem 2. The goal of this problem is to translate some assertions about binary strings into logic notation. The domain of discourse is the set of all ﬁnite-length binary strings: λ , 0, 1, 00, 01, 10, 11, 000, 001, .... (Here λ denotes the empty string.) In your translations, you may use all the ordinary logic symbols (including = ), variables, and the binary symbols 0 , 1 denoting 0, 1. A string like

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## This note was uploaded on 05/27/2011 for the course CS 6.042J taught by Professor Prof.albertr.meyer during the Spring '11 term at MIT.

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MIT6_042JS10_lec06_prob - Massachusetts Institute of...

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