Mathematical logic defines statements as declarative sentences that are either true or false. Simple statements convey a single idea, while compound statements convey two or more ideas joined by logical connectives like "and", "or", and "if-then". The truth value of a simple statement is either true or false, while the truth value of a compound statement depends on the truth values of its simple statements and connectives, as represented in a truth table.

1. Mathematical Logic

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Definition. A statement is a
declarative sentence that is
either true or false, but not
both true and false.

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Example:
Determine whether each sentence is a statement.
5
3
2 

2. Metro Manila is the largest city of the Philippines by
land area.
1. Ampayon is a barangay of Butuan City.
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5. Butuan City is the best city.
6. Help!
7. Where were you?
8. The rain in Cabadbaran City.
9. This sentence is false.
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
x
(an exclamation)
(Subjective)
(A question)
( Not a sentence)
(neither true nor false)
(open sentence)

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Definition.
A simple statement is a statement that
conveys a single idea.
A compound statement is a statement
that conveys two or more ideas.

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If two or more
statements are joined,
or connected, then we
can form compound
statements.
These compound
statements are joined by
logical connectives
“and”, “or”, “if then”, and
“if and only if”.
LOGICAL CONNECTIVES

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Statements are represented symbolically by lowercase letters (e.g., and )
and new statements can be created from existing statements in many ways.
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, r
q
p s

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Definition.
The truth value of a simple statement is
either true (T) or false (F).
The truth value of a compound statement
depends on the truth values of its simple
statements and its connectives.

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A truth table is a table that shows the
truth value of a compound statement for
all possible truth values of its simple
statements.

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