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?
Free to Join!
StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
  • Easily See Your Progress

    We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
  • Make Use of Our Learning Aids

    Last Viewed
    Practice Accuracy
    Suggested Tasks

    Get quick access to the topic you're currently learning.

    See how well your practice sessions are going over time.

    Stay on track with our daily recommendations.

  • Earn Achievements as You Learn

    Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
  • Create and Customize Your Avatar

    Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
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.