Discrete Mathematics Homework 3

Discrete Mathematics Homework 3 - Discrete Mathematics...

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Discrete Mathematics Tawashia Graham Homework Week 3 Homework Using your text complete the following: Page Question Number(s) 79 1a, 1b, 1d, 1e, 2a, 2b, 2c, 12, 13, 16a, 16b, 19b 86 1b, 5, 6a, 6b, 9c, 9e, 9g, 11b, 11c, 19a, 19b Page 79 1- Determine whether each of the following relations is a function with domain (1, 2, 3, 4). For any relation that is not a function, explain why it isn’t. a) [BB] f = { (1, 1), (2, 1), (3, 1), (4, 1), (3, 3)} Not a function: f contains two different pairs of the form ( 3, -) b) f= {(1, 2), (2, 3), (4, 2)} Not a function with a domain {1, 2, 3, 4}. There is no pair of the form (3, -) d) f= {(1, 1), (1, 2), (1, 3), (1, 4)} Not a function. There is more of the one pair of the form (1, -); there are four e) f= {(1, 4), (2, 3), (3, 2), (4, 1)} This is a function. 2- Suppose A is the set of students currently registered at the University of Calgary, B is the set of professors at the University of Calgary, and C is the set of courses currently being offered at the University of Calgary. Under what conditions is each of the following a function? a) [BB] {(a, b) | a is taking course from b} [BB] This is not a function unless each student at the University of Calgary has just one professor, for if student a is taking courses from professors b 1 and b 2 the given set contains (a,b 1 ) and (a , b 2 ) b) {(a, c) | a’s first class each week is in c} This is a function, assuming every student at University of Calgary is taking at least one course c) {(a, c) | a has a class in c on Friday afternoon} Assuming some student a has no class on
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Discrete Mathematics Homework 3 - Discrete Mathematics...

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