Discrete Mathematics I
MATH/CSCI 2112 Solutions to Practice Problems 2 Feb 2016
Counting Examples:
(1) How many distinct 5-digit numbers, between 20000 and 50000, can be formed using
the digits 1, 2, 3, 4, 5, 6 such that no digits repeat. (Hint: For this

Discrete Mathematics I
MATH/CSCI 2112 Assignment 5 Due: Mon 7 March 2016 (hard deadline)
(1) (a) In the previous assignment, you showed: a2 even a even.
Use the result to show a3 even a even.
ANSWER:
a3 even i .e.(a2 a) even
(a2 even a even) But we know,

Discrete Mathematics I MATH/CSCI 2112 Lecture 22-25/01
Counting Read Ch. 3 Sec 3.1 - 3.3 BoP
Count of subsets
How many subsets of does a set of n elements have?
S = cfw_s1 , s2 , . . . sn
n
0
1
2
Subsets
# subsets
cfw_
1 = 20
cfw_, cfw_s1
2 = 21
cfw_,

Discrete Mathematics I MATH/CSCI 2112
Lecture 27-29 /01/16 Counting 2
One more PHP problem:
Ex. In a class of n students, show that there must be at least two students
with the same number of friends in the class (friendship is a reflexive relationship).

Lecture Summary: 18-20/01/16 MATH/CSCI 2112 Winter 2016
Quantifiers
A proposition that has variables into which we can substitute values is called a
predicate. The truth value of the predicate depends on the values substituted
Ex. Q(n) : n2 + n + 41 is p

THE IMPLICATIONS OF IMPLICATIONS
MATH/CSCI2112
02 Lec 08/01
e.g. To review why an implication (p q) is true when both
the antecedent/premise (p) and the consequent/conclusion (q) are both false:
Consider that I say: If this card is a Heart then it is a Qu