16.3. Negative Statements http://www.ck12.org
16.3 Negative Statements
Here you will negate statements and use graphical representations and set theory to explore the implications of
negative statements. You will also learn about De Morgan’s Law.
In everyday speech, negative statements are often ambiguous or unclear. Mathematically, you need a precise way to
negate statements so that you can accurately determine whether statements are true or false. When is the negation of
the following sentence true?
If I am not cold then it is not snowing.
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/63158http://www.youtube.com/watch?v=hfz1gAoNd1w James Sousa: Showing Statements are Equivalent
Guidance
While in everyday language the opposite of “dog” might be “cat”, in mathematics the opposite of “dog” is “not a
dog”. Using the word “not” is the basic way to negate an atomic sentence. An atomic sentence is a logical statement
without logical connectives that has a truth value.
- Original sentence(D):That thing is a dog.
- Negation of sentence(∼D):That thing is not a dog.
The box below represents the universe of all things. This universe can be separated into things that are dogs and
things that are not dogs.