Propositional Logic 2 Flashcards
Covers more applications of propositional logic in context, including contextual examples of questions, truth tables, syntax trees and the distinction between propositions and formulae
describe - in words - the only time that ‘p ⇒ q’ is false
when the antecedent is true but the consequence is false
‘if’ mid-sentence corresponds to…?
⇐
‘only if’ corresponds to….?
⇒
If the lecturer hadn’t shown up last week, Plato would have
given the lecture.
¬S ⇒ P
Exactly one of the following happened: David won or
Victoria won or it was a tie.
(D ∧ ¬V ∧ ¬T ) ∨ (V ∧ ¬D ∧ ¬T ) ∨ (T ∧ ¬D ∧ ¬V )
In the context of the implication p ⇒ q, p is referred to as the…?
premise
In the context of the implication p ⇒ q, q is referred to as the…?
conclusion
difference between a proposition and a formula
propositions are the declarative statements. formulae use propositional variables to represent propositions and/or their relationships with one another
what are the 2 types of formulae…?
atomic and compound
atomic formulae do not contain any…?
propositional connectives
what are the 2 components of atomic formulae…?
the two truth constants (true and false) and propositional variables
another word for equivalence
biconditionality
compound formulae
formulae (compound or atomic) linked by connectives
order of precedence of the 5 propositional connectives
⌐, ∧, ∨, ⇒, ⇔
if an expression contains multiple propositional connectives of the same order of precedence, operations are evaluated from…?
right to left
in syntax trees, the leaf nodes are…?
the propositional variables
in syntax trees the parent nodes are…?
the propositional connectives
the root of the syntax tree
the propositional connective that was applied last
a set of propositions is consistent when…?
it is logically possible for all propositions to be true at the same time
consistency vs validity | deals with…?
the coexistence of propositions vs the relationship between premises and conclusion in an argument.
consistency vs validity | applies to…?
a set of propositions or statements vs arguments composed of premises and a conclusion
the capital latter ‘P’ wou;d refer to the
Propositional statement
how to express XOR in propositional logic
p ⇔ ¬q (or similarly q ⇔ ¬p)
NAND connective symbol
p| q
NOR connective symbol
p ↓ q
how to express a NAND relationship in propositional logic
¬(p ∧ q)
how to express a NOR relationship in propositional logic
¬(p ∨ q)
synonym for formula
well formed formula
is P, the propositional variable, also a propositional formula? why/why not?
yes - propositional variables are SIMPLE propositional formulae
syntax trees make it clear how the expression should be ________.
parsed
