# Statements

##### Introduction
###### Lessons
1. Statements Overview:
2. Statements, and Truth value
3. Statements, and Truth value
##### Examples
###### Lessons
1. Truth value of a Statement

Determine the truth value of each statement:

1. December is the first month of the year.
2. The diameter of a circle is twice the length of the radius.
3. The sums of the squares of the legs of a right triangle are equal to the square of the hypotenuse.
4. $10\times 2+7=90$
5. A hexagon is a six-sided polygon.
2. Variables of Open Sentences

Determine the variable of each open sentence:

1. $2x+5=10$
2. He is very short
3. It is a multiple of 7
4. $2t \leq 2$
5. 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:
1. It has more than four sides
2. It has less than four sides
3. It has exactly 4 sides
4. It has to have 4 sides equal in length
5. It is a rectangle
6. It has interior angles which sum up to 180° degrees
7. 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.

1. $x+7=10$
2. $2+7=10$
3. Soccer is a team sport.
4. $19-4$
6. Huh?
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###### Topic Notes
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.