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Propositions

The document introduces propositions as declarative sentences that can be classified as either true or false. It provides examples of both propositions and non-propositions, highlighting the characteristics that distinguish them. Additionally, it mentions the use of letters to represent propositional variables.

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16 views1 page

Propositions

The document introduces propositions as declarative sentences that can be classified as either true or false. It provides examples of both propositions and non-propositions, highlighting the characteristics that distinguish them. Additionally, it mentions the use of letters to represent propositional variables.

Uploaded by

jastrime
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as TXT, PDF, TXT or read online on Scribd
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Propositions

Our discussion begins with an introduction to the basic building blocks of logic—
propositions.
A proposition is a declarative sentence (that is, a sentence that declares a fact)
that is either true
or false, but not both.
EXAMPLE 1 All the following declarative sentences are propositions.
1. Washington, D.C., is the capital of the United States of America.
2. Toronto is the capital of Canada.
3. 1 + 1 = 2.
4. 2 + 2 = 3.
Propositions 1 and 3 are true, whereas 2 and 4 are false. ▲
Some sentences that are not propositions are given in Example 2.
EXAMPLE 2 Consider the following sentences.
1. What time is it?
2. Read this carefully.
3. x + 1 = 2.
4. x + y = z.
Sentences 1 and 2 are not propositions because they are not declarative sentences.
Sentences 3
and 4 are not propositions because they are neither true nor false. Note that each
of sentences 3
and 4 can be turned into a proposition if we assign values to the variables. We
will also discuss
other ways to turn sentences such as these into propositions in Section 1.4. ▲
We use letters to denote propositional variables (or statement variables), that is,
variables that represent propositions, just as letters are used to denote numerical
variables. The

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