Assessing Truth and Claims Flashcards
*PROPOSITIONS
*Truth- functional connectives:
KEY ELEMENTS OF PROPOSITIONAL LOGIC
also known as sentential
logic or statement logic, is a branch of logic that
deals with propositions and their logical
relationships. In propositional logic, propositions
are statements that can either be true or false.
PROPOSITIONAL LOGIC
A ______is a declarative statement that has a truth
value, meaning it is either true or false.
Example:
“The sky is blue.”
“It is raining outside.”
PROPOSITIONS:
A simple, indivisible statement with no
connectives (like “AND,” “OR,” etc.). It
asserts just one thing.
Example
The floor has been mopped.
The sky is blue
TYPES OF PROPOSITION
Atomic Proposition
A statement that combines two or more atomic
propositions using logical connectives (e.g., “AND,”
“OR,” “IF…THEN”).
Example
The floor has been mopped “and” the
dishes
have been washed.
TYPES OF PROPOSITION
Complex Proposition
These are the logical tools we use to connect
propositions in meaningful ways. Propositional
logic uses connectives to combine simpler
propositions into more complex ones.
Truth- functional connectives:
*CONJUNCTION
*DISJUNCTION
*NEGATION
*CONDITIONAL
*BICONDITIONAL
FUNDAMENTAL
OPERATIONS IN
PROPOSITIONAL LOGIC
OR, symbol: V
Combines two propositions and is true if at
least one of the propositions is true.
Example: “p ∨ q” is true if either p or q (or
both) are true.
Example: “It is raining, or it is sunny.”
DISJUNCTION
AND, symbol: ∧
Combines two propositions and is true only if
both propositions are true.
Example: “p ∧ q” is true if both p and q are
true.
Example: “It is raining, and it is cold outside.”
CONJUNCTION
NOT, symbol: ¬
Inverts the truth value of a proposition.
Example: “¬p” is true if p is false, and vice
versa.
Example: “It is not raining.”
NEGATION
IF…THEN, symbol: →
Represents a logical implication. It says that if one
proposition (the antecedent) is true, then the other (the
consequent) must also be true.
Example: “p → q” is true if whenever p is true, q is also
true.
Example: “If it rains, then the ground will be wet.”
CONDITIONAL
IF AND ONLY IF, symbol: ↔
This indicates that the two propositions have the same truth
value: both are either true or false.
Example: “p ↔ q” is true if p and q are either both true or
both false.
Example: “The light is on if and only if the switch is
flipped.”
BICONDITIONAL
A __________ is a systematic way to represent the
truth values of propositions and their combinations.
o
It lists all possible truth values for propositions and
shows how these truth values interact through logical
connectives.
truth table
WHAT IS THE IMPORTANCE OF
STUDYING PROPOSITIONAL LOGIC?
Propositional logic is a vital component of logical
reasoning, with significant applications in
mathematics, computer science, philosophy, and
beyond. Its principles enable structured thinking and
effective problem-solving across various domains.
