Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

  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.