Negations

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Introduction
Lessons
  1. Negations Overview:
    Definition of Negations and Examples
Examples
Lessons
  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.
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    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.