Republic of the Philippines
BATANGAS STATE UNIVERSITY
College of Informatics and Computing Sciences
Golden Country Homes, Barangay Alangilan
Batangas City, Batangas 4200
Lecture Module
Discrete Mathematics (CpE 405)
Propositions Logic and Related Concepts
Propositional Logic
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A statement is a declarative sentence that can be True (1) or False (0).
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Example:
1. Milk is white
2. 1Ø1 = 0
3. Humans are just fish with legs
Syntax
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Propositions are denoted with capital letters P, Q, R
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Lowercase letters p, q, r is used for general propositions that have no meaning.
•
used them for general proofs
Connectives
This all connectives are a well-formed formula (wff) of wolf.
1.
2.
3.
4.
5.
6.
p
¬p
p∧q
p∧q
p→q
p⇔q
Connectives
1. OR (∨) - The OR operation of two propositions A and B.
- (written as A V B) is true if at least any of the propositional variable A or B is
true.
Truth Table Example:
2. AND (∧) - The AND operation of two propositions A and B
- (written as A ∧ B) is true if both propositional variable A and B is true.
Truth Table Example:
3. Negation/ NOT (¬) – The negation/not of a proposition A (written as ¬A) is false when A
is true and is true when A is false.
Truth Table Example:
4. Implication / if-then (→) – An implication A→B is the proposition “if A, then B”. It is
false if A is true, and B is false. The rest cases are true.
Truth Table Example:
5. If and only if (⇔) - A⇔B is bi-conditional logical connective which is true when p and q
are same, i.e. both are false or both are true.
Truth Table Example: