The Connecting

1
The Connecting Words
Chapter 6 Reasoning
6.4
6.4.1
MATHPOWERTM 11, WESTERN EDITION
2
Compound Statements
Proving theorems in mathematics involves making
logical connections between statements and their
conclusions.
A statement is a sentence that is either true or
false.
A. Archbishop OLeary is a high school. B.
Archbishop OLeary is an elementary school. C.
Archbishop OLeary is the best school in the city.
Sentence A is a true statement. Sentence B is a
false statement. Sentence C is not a statement
because it is an opinion and is neither true nor
false.
Simple statements can be combined to form a
compound statement by connecting one or more
statements with a connective, such as and,
or, and not.
6.4.2
3
Using and
For a compound statement to be true, both parts
of the statement must be true,
because and is inclusive.
Calgary won last night. Edmonton won last night.
Calgary and Edmonton won last night.
x is a factor of 48 and x is a factor of 30.
The compound statement is true for factors that
satisfy both statements.
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16,
24, 48. The factors of 30 are 1, 2, 3, 5, 6, 10,
15, 30.
The factors of 48 and 30 are 1, 2, 3, and 6.
This region represents factors of 30 and factors
of 48
8
5
A Venn diagram can be used to illustrate this
example. The numbers that are factors of 48 and
factors of 30 are within the region of overlap.
1
4
10
2
16
12
15
3
6
48
30
24
6.4.3
Factors of 48
Factors of 30
4
Using a Number Line to Graph Compound and
Statements
On a number line, indicate the numbers described
by the statement
x gt 3 and x lt 8.
x gt 3
x lt 8
x gt 3 and x lt 8
6.4.4
5
Using or
For a compound statement to be true, at least one
of the two parts (or both parts) must be true.
x is a factor of 48 or x is a factor of 30.
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16,
24, and 48. The factors of 30 are 1, 2, 3, 5, 6,
10, 15, and 30.
The compound statement is true for factors that
satisfy either statement or both statements.
The factors are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15,
24, 30, and 48.
The factors are factors of 48 or factors of 30
or factors of both.
8
5
4
1
16
10
2
12
3
15
6
48
24
30
Factors of 48
Factors of 30
6.4.5
6
Using a Number Line to Graph Compound or
Statements
On a number line, indicate the numbers described
by the statement
x lt 3 or x gt 8.
x lt 3
x gt 8
x lt 3 or x gt 8
6.4.6
7
Using not

• When using not, you are writing a
• negation of the related true statement.
• When a statement is true, its negation
• is false and vice versa.

On a number line, indicate the numbers described
by each statement
a) x ? 2.5
b) x lt 2.5
6.4.7
8
1. Calculate the number of students in
each subject.
Venn Diagrams
M - 44
P - 35
C - 33
2. Calculate the number of students
taking a) math and physics
15
b) physics and chemistry.
12
c) math and chemistry.
13
d) all three subjects.
10
e) math or physics.
64
f) physics or chemistry.
56
3. Calculate the total number of students.
82
6.4.8
9
Using a Venn Diagram to Solve a Problem
Each member of a sports club plays at least one
of the following sports soccer, rugby or
tennis. The following information is given a)
163 play tennis 36 play tennis and rugby
13 play tennis and soccer b) 6 play all three
sports 11 play soccer and rugby 208 play
rugby or tennis c) 98 play soccer or rugby
Use this information to A) draw a Venn
diagram. B) determine the number of members in
the club.
6.4.9
10
Using a Venn Diagram to Solve a Problem contd
Rugby
Soccer
5
10
40
6
30
7
120
There are 218 members in the club.
Tennis
6.4.10
11
Assignment
Suggested Questions
Pages 354-356 1-45 odd, 47-50, 51, 54ace, 55,
56, 57
6.4.11