Propositional Logic - Syntax and Semantics Flashcards
By the end of this deck, learners will be proficient in understanding and applying the syntax and semantics of propositional logic. They will be able to accurately use symbols and notation, determine truth values through truth tables, and apply logical connectives (AND, OR, NOT, IF...THEN, IFF) to construct and analyze logical expressions and arguments.
What is propositional logic?
Propositional logic is a branch of logic that deals with propositions and their combinations using logical connectives.
What symbols are commonly used in propositional logic?
Common symbols include variables (p, q, r…), logical connectives (∧, ∨, ¬, →, ↔), parentheses, and sometimes constants for truth (T) and falsity (F).
What is the truth value in propositional logic?
A truth value is the value indicating the truth or falsity of a proposition, typically denoted as true (T) or false (F).
How is a truth table used in propositional logic?
A truth table displays the truth values of propositions under all possible truth value combinations of their atomic components.
What does the logical connective AND (∧) signify?
The AND connective (∧) signifies conjunction and yields true if and only if both operands are true.
Explain the OR (∨) connective in propositional logic.
The OR connective (∨) signifies disjunction and yields true if at least one of the operands is true.
Define the NOT (¬) connective.
The NOT connective (¬) signifies negation, inverting the truth value of its operand (¬T = F, ¬F = T).
What is the implication (→) in propositional logic?
The implication (→) connective signifies conditional relation, yielding false only when the antecedent is true, and the consequent is false.
Describe the biconditional (↔) connective.
The biconditional (↔) connective signifies equivalence, yielding true if both operands are equally true or false.
How do you determine the truth value of a complex proposition using a truth table?
To determine the truth value, list all possible truth values of atomic propositions and compute the truth values of the complex proposition step by step for each combination.
What is the significance of parentheses in propositional logic?
Parentheses determine the order of operations in complex logical expressions, ensuring clarity and precision in evaluating propositions.
How can you represent a tautology in propositional logic?
A tautology can be represented by a logical statement that is always true, regardless of the truth values of its constituent propositions.
What is a contradiction in propositional logic?
A contradiction is a proposition that is always false, regardless of the truth values of its constituent components.
Give an example of a logical equivalence using basic connectives.
An example of logical equivalence is
p→q being equivalent to ¬p∨q.
