Propositional Logic 3 Flashcards
Covers how tautologies & contradictions can be used to and the algebraic laws of propositional logic
metavariables
expressions in meta-languages that represent arbitrary formulae
when can a formula be neither a tautology or contradiction
when there is a combination of T and F in the output column
in the WFF p ⇒ q, p is the p____?
premise
in the WFF p ==> q, q is the c_______?
conclusion
the implication symbol is ______ associative
right
is the equivalence symbol associative?
yes
is the conjunction symbol associative?
yes
is the implication symbol associative?
NO
describe the law of replication
p ⇒ q therefore i’m either not p or i’m q
describe the contrapositive in words
the negation of the conclusion implies the negation of the premises
each of the algebraic laws are in themselves a …?
tautology
what is short-circuiting
skipping the evaluation of the second part of a boolean expression in a conditional statement if the first part is enough to determine the result
benefit of short-circuiting
optimises and can speed up the execution of code
disadvantage of short-circuiting
can cause unexpected problem if the right hand side of the short-circuited expression has a side effect that is important (but not executed)
name of this algebraic law:
p ∨ q ⇔ q ∨ p
commutativity
name of this algebraic law:
p ∧ (q ∨ r) ⇔ (p ∧ q) ∨ (p ∧ r)
distributivity
name of this algebraic law:
⌐(p ∧ q) ⇔ ⌐p ∨ ⌐q
de Morgan’s Law
name of this algebraic law:
⌐(⌐p) ⇔ p
double negation
name of this algebraic law:
p ∧ true ⇔ p
tautology
name of this algebraic law:
p ∨ true ⇔ true
tautology
name of this algebraic law:
p ∨ false ⇔ p
contradiction
name of this algebraic law:
p ∧ false ⇔ false
contradiction
name of this algebraic law:
p ∨ (q ∨ r) ⇔ (p ∨ q) ∨ r
associativity
name of this algebraic law:
p ∨ p ⇔ p
idempotence