# Statements

### Statements

#### Lessons

Notes:

A statement (closed sentence) is a sentence that is either true or false, but not both. We can denote each statement as a letter. For example,
$p$: 1 cm is exactly equal to 10 mm
If we can determine the truth or falsity of a statement, then it has a truth value. An open sentence is a sentence that has a variable. The truth value depends on that variable.
The Domain (or replacement set) is a list of elements that can be used to replace the variable.
The truth set is the list of elements from the domain that makes the open sentence true.
• Introduction
Statements Overview:
a)
Statements, and Truth value

b)
Statements, and Truth value

• 1.
Truth value of a Statement

Determine the truth value of each statement:

a)
December is the first month of the year.

b)
The diameter of a circle is twice the length of the radius.

c)
The sums of the squares of the legs of a right triangle are equal to the square of the hypotenuse.

d)
$10\times 2+7=90$

e)
A hexagon is a six-sided polygon.

• 2.
Variables of Open Sentences

Determine the variable of each open sentence:

a)
$2x+5=10$

b)
He is very short

c)
It is a multiple of 7

d)
$2t \leq 2$

e)
She likes to go for long walks

• 3.
Use the domain {triangle, rectangle, square, parallelogram, pentagon, hexagon} to find the truth set for each open sentence:
a)
It has more than four sides

b)
It has less than four sides

c)
It has exactly 4 sides

d)
It has to have 4 sides equal in length

e)
It is a rectangle

f)
It has interior angles which sum up to 180° degrees

g)
It only has right angles

• 4.
Open sentence, statement, or neither?

Are the following sentences an open sentence or a closed sentence (statement), or neither? If it is an open sentence, find the variable. If it is a statement, then find the truth value.

a)
$x+7=10$

b)
$2+7=10$

c)
Soccer is a team sport.

d)
$19-4$

e)