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. Negations Overview:
    Definition of Negations and Examples
  1. Negation of the Statement

    Write the negation of each statement:

    1. The sun rises from the east.
    2. 1+1=0 1+1=0
    3. January is the first month of the year.
    4. The Eiffel Tower is in Japan.
    5. A square has 7 sides.
  2. Truth Value of a Negation

    Write the negation of each statement, and determine the truth value:

    1. A snake is a reptile.
    2. The measure of an acute angle is greater than 90°.
    3. 5+5+5=555 5+5+5=555
    4. 56\frac{5}{6} is a fraction.
  3. The symbols represent the following statements

    pp: A pentagon has 5 sides
    qq: United States is a city
    rr: Chairs have four legs

    Write a complete sentence in words to show what the symbols means, and find the truth value:

    i) ~pp
    ii) ~qq
    iii) ~rr
    1. Double Negation

      Determine the truth value of the statement. Negate it twice, write it in a complete sentence, and determine the new truth value:

      1. A quarter of an hour is 15 minutes
      2. There is caffeine in coffee.
      3. The ocean has salt water.
    Topic Notes
    The negation of a statement is the opposite of a statement. We denote it with either "not" or the symbol ~. The negation gives the opposite of the truth value. For example,
    pp: A square is a rectangle
    ~ pp: A square is not a rectangle pp is true, so ~pp is false.