Proposition Flashcards
Truth table for a proposition with n distinct variables has how many rows?
2^n rows
meaning of: p –> q
what is the contrapositive of
p –> q
~q –> ~p
converse of p–>q
q–>p
T/F a implication and its contrapositive always have the same value?
True
whats p<–>q
biconditional
p if and only if q
p iff q
p is a necessary and sufficient condition for q
precedence
right-associative
negation applied first
what is a tautology
proposition where its truth value is always true
what is a contradiction?
proposition is always false
what is the three — signal?
truth table
what is satisfiability
at least one possible true outcome
what is predicate logic?
some property holds true for some set of objects
statement that involves one or more variables whose truth value depends on the values assigned to those variables
how denote a predicate
P(x, y)
looks like a function
Universal quantification - every element of some collection has a particular property
no value where P(x) is false
existential quantitifcation
there’s at least one value of x where P(x) is true
De Morgans law to negating quantifiers
restrict domain
x^2 > 0
common abuse of formal notation in first. Use the second.
