Negations

Negations

Lessons

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.
  • Introduction
    Negations Overview:
    a)
    Definition of Negations and Examples


  • 1.
    Negation of the Statement

    Write the negation of each statement:

    a)
    The sun rises from the east.

    b)
    1+1=0 1+1=0

    c)
    January is the first month of the year.

    d)
    The Eiffel Tower is in Japan.

    e)
    A square has 7 sides.


  • 2.
    Truth Value of a Negation

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

    a)
    A snake is a reptile.

    b)
    The measure of an acute angle is greater than 90°.

    c)
    5+5+5=555 5+5+5=555

    d)
    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

  • 4.
    Double Negation

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

    a)
    A quarter of an hour is 15 minutes

    b)
    There is caffeine in coffee.

    c)
    The ocean has salt water.