hw2cs - CSE 20 Discrete Mathematics Fall 2010 Problem Set 2...

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CSE 20: Discrete Mathematics Fall 2010 Problem Set 2 Instructor: Daniele Micciancio Due on: Wed. Oct. 13, 2010 Problem 1 (6 points) For each of the following statements (a) formulate the statement in English without using mathematical symbols, (b) write the logical negation of the statement (this time using only logical and mathematical notation) but without using the ¬ symbol, and (c) say whether the original statement or its negation is true providing a brief justiﬁcation for your answer. 1. x Z . y Z .x < y 2. y Z . x Z .x < y (For part (b), you can use the fact that for any two integers x,y , the negation of x < y is x y .) Problem 2 (8 points) In this problem, all variables range over the integers. Recall that “ x divides y ” (in symbols x | y ) if c. ( y = c · x ) . Formulate the following statement using the language of predicate logic (you can use the relation x | y as an abbreviation), and prove that it is correct. Statement: “For any

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hw2cs - CSE 20 Discrete Mathematics Fall 2010 Problem Set 2...

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