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