Math 2230
Test #1 Solutions
1. Let A be a collection of sets, and R the relation on A given by (X, Y ) R
if and only if X Y . Show that R is a partial order.
[3 marks]
Answer:
For any set X, X X which implies (X, X) R for all X A. Hence,
R is reflexive.
S
Math 2230
Test #2
Name:
1. How many permutations of the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, are there
in which none of the digits 1, 2, 3, 4 and 5, are in their original place?
[5 marks]
Answer:
Let S be the set of all permutations of 1, 2, 3, 4, 5, 6
Math 2230
Tutorial 5:Solutions
1. How many ways are there to hand out 24 cookies to three children so that they each
get an even number, and they at each get least 2 and no more than 10? Use generating
functions.
Want
of x24 in g(x) = (x2 +x4 +x6 +x8 +x10
Math 2230
Assignment # 1 Solutions
1. Let A = cfw_1, 2, 4 and let R be the relation on A A defined by (a, b)R(c, d) iff ad = bc.
(a) Show that R is an equivalence relation on A.
Answer:
Reflexive: Since ab = ba for any a and b, it follows that (a, b)R(a.
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Math 2230
Assignment # 2 Solutions
1. A bakery sells 3 types of donuts; Long John, Boston Cream, and Cholcolate Glaze. If the
bakery has 3 Long Johns, 5 Boston Creams, and 7 Chocolate Glazed, how many ways are
there to order 12 donuts?
Solution:
Let S be