Propositional Logic Flashcards
(14 cards)
a statement that can either be true or false and must be a declarative sentence
Proposition
or “propositional statement”
if a proposition is composed of two or more propositions
Complex Proposition
Types of Complex Propositions
uses the connective “and”
using the symbol “^”, as in “p ^ q”
Conjunction
determining the truth value of a conjunction
true if and only if p and q are both true
if both propositions are false or at least one of the propositions is true, then it is false
Types of Complex Propositions
uses the connective “or”
using the symbol “∨”, as in “p ∨ q”
Disjunction
determining the truth value of a disjunction
true if at least one proposition is true or both propositions are true
if both are false then it is false
Types of Complex Propositions
the “opposite” of a proposition
using the symbols “~” (~p) or “¬” (¬p)
Negation
determining the truth value of a negation
opposite of the truth value of the original proposition
if p is TRUE, then ¬p is FALSE
Types of Complex Propositions
if and then statement, or p implies q
using the symbol “→”, as in “p → q”
Conditional Statement
also known as “logical implication”
Conditional Statement
the first proposition in a conditional statement
p in “p → q”
Hypothesis
Conditional Statement
the second proposition in a conditional statement
q in “p → q”
Conclusion
determining the truth value of a conditional statement
true if both propositions have the same truth value, or if the hypothesis is false
Types of Complex Propositions
uses the connective “if and only if”
using the symbols “⟺” (p ⟺ q) or “iff” (p iff q)
Biconditional Statement
determining the truth value of a biconditional statement
true if both propositions are true or both propositions are false
