# tut3 - Problems to Week 4 Tutorial MACM 101 1. Consider a...

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Problems to Week 4 Tutorial — MACM 101 1. Consider a universe which is the set of all polygons with three or four sides, and the following predicates for this universe: A ( x ): all interior angles of x are equal; E ( x ): x is a equilateral triangle; H ( x ): all sides of x are equal; P ( x ): x has an interior angle that exceeds 180 ; Q ( x ): x is a quadrilateral; R ( x ): x is a rectangle; S ( x ): x is a square; T ( x ): x is a triangle. Translate each of the following statements into an English sentence, and determine whether the statement is true or false. (a) x ( Q ( x ) T ( x )); (b) x ( T ( x ) P ( x )); (c) x ( Q ( x ) ∧ ¬ R ( x )); (d) x ( H ( x ) E ( x )); (e) x ( S ( x ) ( A ( x ) H ( x ))). 2. Let P ( x,y ) ,Q ( x,y ) denote the following predicates P ( x,y ) : x 2 y Q ( x,y ) : x + 2 < y. If the universe for each of x,y consists of all real numbers, determine the truth value for each of the following statements (a) P ( -

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## This note was uploaded on 12/12/2010 for the course MACM 201 taught by Professor Marnimishna during the Fall '09 term at Simon Fraser.

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tut3 - Problems to Week 4 Tutorial MACM 101 1. Consider a...

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