02/18/2008 MTH 220 (201)
STUDY SHEET for MIDTERM #1 (Monday, February 25)
- Ch. 1 (1.1 – 1.5)
- Ch. 2 (2.1, 2.2)
- Ch. 3 (3.1, 3.2, 3.3)
The best way to prepare to the midterm is to read the book and to do the homework
exercises. Please, take time to go over the material.
Here is what you have to have an idea about:
1. Sets and Subsets.
a) Special sets: Z+, N, Z, Q, and R.
b) Empty set.
c) Finite and infinite sets. Cardinality of a set.
d) Power set.
e) Venn diagrams.
2. Operations on Sets
a) Union of two sets.
b) Intersection of two sets.
c) Disjoint sets.
d) Complement of B with respect to A.
e) Complement of a set.
f) Symmetric difference of two sets.
g) Algebraic properties of set operations (commutative, associative, distributive,
etc.). De Morgan’s laws.
h) The addition principle.
3. Sequences
a) Finite and infinite sequences.
b) Recursive and explicit formulas.
c) Set corresponding to a sequence.
d) Characteristic functions and its properties.
e) Computer representation of sets and subsets by using characteristics functions.
f) Countable and uncountable sets.
4. Properties of Integers
a) Prime numbers.
b) Greatest common divisor (GCD) and its properties.
c) Relatively prime numbers.
d) Euclidean Algorithm to find GCD.
e) Least common multiple (LCM). Relationship between GCD and LCM.
