Terminology
A collection of objects which can be letters, numbers, or words.
Set
The most commonly used type of real number is called what?
Natural Numbers or Counting Numbers
What is the set operation that says that everything in the first set is also in the other set, but the sets cannot be exactly the same. Also write its symbol.
Proper Subset
Determine is the given sentences are statements? yes or no
a) 13+5 = 17
b) Turn the light off in the kitchen.
c) The Houston Texans are an undefeated team.
a) Yes, it is a false statement.
b) No, this is a command.
c) Yes, it is a false statement.
What is used to summarize possible truth values for statements?
A truth table
The number of elements (objects) in a set often denoted as n(set).
Cardinal Number
What is the difference between the natural numbers and the whole numbers?
The whole numbers include the number zero.
a) What is the formula to find the number of subsets?
b) What is the formula to find the number of proper subsets?
a) 2n
b) 2n - 1
Negate the following statement:
The most commonly sold ice cream flavor at Baskin Robbins is chocolate.
The most commonly sold ice cream flavor at Baskin Robbins is not chocolate.
When is the conditional statement p → q false?
When the first statement is TRUE and the second statement is FALSE.
A type of set where the number of elements can be counted; there is a definite end point.
Finite Set
Using the roster method write the set R of odd natural numbers between 2 and 16. List all elements of the set.
R = {3,5,7,9,11,13,15}
Given the sets below, identify them as equal, equivalent, both, or neither.
T = {a, t, p, o}
S = { p, o, a, t, o}
Both
What 4 things are not considered a statement? Must name all 4 in any order.
questions, commands, exclamations, opinions
Determine the overall truth value of the compound statements below:
a) An octopus has eight legs, and a bird can fly.
b) If a bird can fly then an octopus does not have eight legs.
c) A bird can fly, or an octopus does not have eight legs.
a) True
b) False
c) True
Sets that have the same number of elements are said to be what type of sets?
Equivalent Sets
Using the roster method write the set B which is the set of integers greater than or equal to -5. List at least the first 6 elements of the set.
B = {-5, -4, -3, -2, -1, 0,...}
Given the sets below, write T intersection S:
U = {1, 6, 8, 14, 21, 22, 28, 80, 96, 99}
T = {1, 8, 14, 21, 22, 80, 99}
S = {6, 28, 96}
The Empty Set
Consider the statements p and q:
p = There are monkeys at the zoo.
q = There are tigers at the zoo.
Write the following using symbolic notation:
a) If there are tigers at the zoo then there are no monkeys at the zoo.
b) There are monkeys at the zoo or there are tigers at the zoo.
a) q → -p
b) p V q
Construct a truth table for the following using p and q as statements.
-p V q
column p: TTFF
column q: TFTF
column -p: FFTT (this column is optional)
SOLUTION column -p V q: TFTT
When the elements of a set cannot be clearly determined, how do we classify the set?
Not Well-Defined
Write the set of even whole numbers 0 to 23. List all elements of the set.
{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22}
Given the sets below, write the complement of set B:
U = {1, 6, 8, 14, 21, 22, 28, 80, 96, 99}
A = {1, 8, 14, 21, 22, 80, 99}
B = {1, 8, 21, 22, 96}
{6, 14, 28, 80, 99}
Given the following statements:
p = You live in Dallas.
q = You live in Texas
Identify each statement below as the converse, inverse, or contrapositive.
a) If you do not live in Texas then you do not live in Dallas.
b) If you live in Texas then you live in Dallas.
c) If you do not live in Dallas then you do not live in Texas.
a) Contrapositive
b) Converse
c) Inverse
Construct a truth table for the following using p and q as statements.
(p ∧ q) → p
column p: TTFF
column q: TFTF
column (p ∧ q): TFFF
SOLUTION column (p ∧ q) → p: TTTT