This document discusses the basics of propositional logic. It defines propositions or statements as the basic units of propositional logic. Compound propositions are formed when simple propositions are connected with logical connectives like "and" and "or". A proposition must always be able to be validated as true or false. It provides examples of true, false, and non-valid propositions. Propositional variables are used to represent unspecified statements. Logical equivalences are compound propositions that have the same logical content. Predicates are parts of statements that can be affected by variables. Quantifiers like universal, existential, and uniqueness are used to represent logical quantities.

2. PROPOSITIONAL LOGIC
Proposition or statements, are also known as simple
sentences makes up the basic units for propositional
logic.
When two or more simple sentences are related
through connectives, it forms a more complicated
proposition called compound sentence.
A statement / propositions must always be able to be
validated as True (T) or False (F).

3. EXAMPLE:
i) All fathers are men.
This statement is true because only man can be father.
ii) All men are father.
This statement is false because only those men who are married
and have kids are fathers. Single men are not father.
iii) I like Monday.
This sentence is neither true nor false as it does not include a
fact. The notion of ‘liking Monday’ is entirely depending on the
particular individual. Some may like it. Some may not.
Sentence which are neither true nor false are not propositions.

4. PROPOSITIONAL
VARIABLES
Propositional variables are used to stand for
unspecified statements. Means that each variable
assigned may or may not have connection between
them.

5. EXAMPLE:
i) She likes dancing.
ii) She likes camping.
Iii) She likes outdoor activities.
Each variable is assigned to a statement.

6. PROSITIONAL
EQUIVALENCE
Tautology
• A compound proposition that is always true
Contradiction
• A compound proposition that is always false
Contingency
• A compound proposition that is neither a tautology nor
a contradiction.

7. EXAMPLE:
LOGICAL EQUIVALENCES
• Compound proposition that have the same logical
content. Means, compound propositions p and q are
called logically equivalent if p ↔ q is a tautology.

8. PREDICATES
In some situations, a statement can be composed of
two parts, the variable and the predicates.

9. EXAMPLE:
The cost of an apple is RM x.
 (In this case, the cost of the apple is a predicate, while x is the
variable which represents the price.)
The above statement can also be expressed as
propositional function P at the value of x, which is
P(x), Where P[the cost of an apple] is affected by x[the
price].
 Note: Predicate is not a proposition until variable is
declared on it. P itself is not a proposition until it is bound
by x, forming P(x).

10. QUADTIFIERS
Universal Quantifier
• ∀ is used to represent ‘for all’
Existential Quantifier
• ∃ is used to represent ‘for some state / value of’
Uniqueness Quantifier
• ∃! Is used to represent ‘for one and only one x’