MIT6_042JF10_assn01

MIT6_042JF10_assn01 - 6.042/18.062J Mathematics for...

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6.042/18.062J Mathematics for Computer Science September 9, 2010 Tom Leighton and Marten van Dijk Problem Set 1 Problem 1. [24 points] Translate the following sentences from English to predicate logic. The domain that you are working over is X , the set of people. You may use the functions S ( x ), meaning that “x has been a student of 6.042,” A ( x ), meaning that “x has gotten an ‘A’ in 6.042,” T ( x ), meaning that “x is a TA of 6.042,” and E ( x, y ), meaning that “x and y are the same person.” (a) [6 pts] There are people who have taken 6.042 and have gotten A’s in 6.042 (b) [6 pts] All people who are 6.042 TA’s and have taken 6.042 got A’s in 6.042 (c) [6 pts] There are no people who are 6.042 TA’s who did not get A’s in 6.042. (d) [6 pts] There are at least three people who are TA’s in 6.042 and have not taken 6.042 Problem 2. [24 points] Use a truth table to prove or disprove the following statements: (a) [12 pts] ¬ ( P ( Q R )) = ( ¬ P ) ( ¬ Q ∨ ¬ R ) (b) [12 pts] ¬ ( P ( Q R )) = ¬ P ( ¬ Q ∨ ¬ R ) Problem 3. [24 points] The binary logical connectives ( and ),
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