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,
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.
  • 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)
    10×2+7=9010\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=102x+5=10

    b)
    He is very short

    c)
    It is a multiple of 7

    d)
    2t2 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=10x+7=10

    b)
    2+7=10 2+7=10

    c)
    Soccer is a team sport.

    d)
    194 19-4

    e)
    Patsy, please leave.

    f)
    Huh?