This document discusses basic concepts in logic and constructing truth tables. It defines a proposition as a declarative sentence that is either true or false. Propositions can be simple or compound, formed using logical connectors like "and", "or", and "if-then". Truth tables show all possible truth value combinations of propositions, with one row per combination. They are used to evaluate propositions with logical operators like negation, conjunction, disjunction, conditional, and biconditional. A truth table for n propositions will have 2n rows, one for each possible combination of true and false values.

1. LOGIC
PROPOSITIONS
LOGICAL OPERATORS
CONSTRUCTING TRUTH TABLES
General Mathematics

2. PROPOSITION
•A proposition is a declarative
sentence that is either true or false,
but not both, If a proposition is true,
then its truth value is true which is
denoted by T; otherwise its truth
value is false and denoted by F.

3. REMARK
•Propositions are usually denoted by
small letters as shown below,
p: Everyone should study logic.

4. EXAMPLE 1:
•Determine whether each of the following
statements is a proposition or not. If a
proposition, give its truth value.
p: Mindanao is an island in the Philippines.
q: Find a number which divides your age.
s: Welcome! to the Philippines.
t: 3+2 = 5
v: What is the domain of the function?

5. PROPOSITION IN MATHEMATICS FORM

7. COMPOUND PROPOSITION
A compound proposition is a proposition formed from
simpler propositions using logical connectors or some
combination of logical connectors. Some logical
connectors involving propositions p and/or q may be
expressed as follows:
• not p
• p and q
• p or q
• if p then q
A proposition is simple if it cannot be broken down any
further into other component propositions.

8. LOGICAL OPERATORS
•Given a proposition, its truth table shows all its
possible truth values.
•Example 1. Since a proposition has two
possible truth values a proposition p would
have the following truth table.

9. TRUTH TABLE
•The rows of the table will correspond to each of
the possible truth value combination of p and
q, and so there will be 22=4 rows.

10. IN GENERAL, A TRUTH TABLE INVOLVING A
PROPOSITIONS HAS 2N ROWS.

11. NEGATION

12. NEGATION

13. CONJUNCTION

14. CONJUNCTION
•Example 3:

15. DISJUNCTION

16. DISJUNCTION

18. CONDITIONAL

19. CONDITIONAL

20. BICONDITIONAL

21. • Versosa, Debbie Marie B. et. al. (2016) Teaching Guide for SHS
General Mathematics, Published by the CHED

22. THANK YOU
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