Expressing Statements Using Predicates and Quantifiers

Learn how to express various statements involving conditions and qualifications using predicates and quantifiers. Examples include defining elite flyers on airlines, qualifying for marathons based on previous times, requirements for earning a master's degree as a student, and identifying students with high credit hours and grades. Understanding these concepts is crucial in discrete mathematics.

• Predicates
• Quantifiers
• Discrete Math
• Statements
• Qualifications

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1. Discrete Math: Predicates and Quantifiers Exercise 19

2. Exercise Express each of these statements using predicates and quantifiers. a) A passenger on an airline qualifies as an elite flyer if the passenger flies more than 25,000 miles in a year or takes more than 25 flights during that year. b) A man qualifies for the marathon if his best previous time is less than 3 hours and a woman qualifies for the marathon if her best previous time is less than 3.5 hours. c) Astudentmusttakeatleast60coursehours,oratleast 45 course hours and write a master s thesis, and receive a grade no lower than a B in all required courses, to receive a master s degree. d) There is a student who has taken more than 21 credit hours in a semester and received all A s.

3. Solution In each case we need to make up predicates. The answers are certainly not unique and depend on the choice of predicate, among other things.

4. References Discrete Mathematics and Its Applications, McGraw-Hill; 7th edition (June 26, 2006). Kenneth Rosen Discrete Mathematics An Open Introduction, 2nd edition. Oscar Le in A Short Course in Discrete Mathematics, 01 Dec 2004, Edward Bender & S. Gill Williamson