1. Statements Overview:
  2. Statements, and Truth value
  3. Statements, and Truth value
  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. 10×2+7=9010\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=102x+5=10
    2. He is very short
    3. It is a multiple of 7
    4. 2t2 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=10x+7=10
    2. 2+7=10 2+7=10
    3. Soccer is a team sport.
    4. 194 19-4
    5. Patsy, please leave.
    6. Huh?
Topic 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,
pp: 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.