Logic and Formality Flashcards
Father of Logic
Aristotle
An expression is completely formal when it is independent and precise.
True
What is a STATEMENT?
main component of logic in mathematics.
Propositional Variable
variable which used to represent a statement.
Formal propositional
written using propositional logic notation, p, q, and r are used to represent
statements.
used to combine simple statements which are referred to as compound statements.
Logical Connectives
statement composed of two or more simple statements connected by logical
Connectives.
compound statement
A statement which is not compound is said to be?
simple (also called atomic).
NEGATION
The negation of the statement p is denoted by ~p, where ~ is the symbol for “not.”
If p is true, ~p is false. Meaning, the truth value of the negation of a statement is always the reverse
of the truth value of the original statement.
True
CONJUNCTION
CONJUNCTION
If p is true and q is true, then p ∧ q is true; otherwise p ∧ q is false. Meaning, the conjunction of two
statements is true only if each statement is true.
True
disjunction of the statement p, q is the compound statement “p or q.”
DISJUNCTION
Symbolically, p ∨ q, where ∨ is the symbol for?
or
If p is true or q is true or if both p and q are true, then p ∨ q is true; otherwise p ∨ q is false. Meaning, the disjunction of two statements is false only if each statement is false.
DISJUNCTION
The conditional (or implication) of the statement p and q is the compound statement “if p then q.”
CONDITIONAL
Symbolically, p → q, where → is the symbol for ?
“if then”
In conditional, p is called hypothesis (or antecedent or
premise) and q is called conclusion (or consequent or consequence).
True
The conditional statement p → q is false only when p is true and q is false; otherwise p → q is true.
Meaning p → q states that a true statement cannot imply a false statement.
True
biconditional of the statement p and q is the compound statement “p if and only if q.”
BICONDITIONAL
Symbolically, p ↔ q, where ↔ is the symbol for ?
“if and only if.”
If p and q are true or both false, then p ↔ q is true; if p and q have opposite truth values, then p ↔ q is false.
BICONDITIONAL
the statement p and q is the compound statement “p exclusive or q.”
EXCLUSIVE-OR
Symbolically, p ⊕ q, where ⊕ is the symbol for ?
“exclusive or.”
If p and q are true or both false, then p ⊕ q is false; if p and q have opposite truth values, then p ⊕ q
is true.
Exclusive-or
