infinite set
set of unlimited elements; ex: all real numbers
cardinality of a power set
2^(|A|)
ordered pairs
(a, b); order is important unlike in a set
entries in n-tuples
the order of elements is crucial; will be multiplied for Cartesian product
proposition
a statement that is either true or false
truth value
the T/F value of a proposition
logical operation
combines propositions with a rule; and, or, if/then
conjunction
and; true if all operands are true
negation
not; negates current truth value
disjunction
or; true if at least one operand is true
truth table
a table listing all outcomes for truth values; what if every element was T/F, one by one
conditional proposition
p -> q; if p, then q; false only if conclusion is false
converse
q -> p; reverse order
inverse
notp -> notq; reverse truth value
contrapositive
notq -> notp; reverse order and truth value
tautology
a statement that is always true
contradiction
a statement that is always false
biconditional operation
p <-> q; p if and only if q; T if all truth values are the same
lambda
concatenating lambda to a string does not change it at all
in p -> q…
p is the hypothesis and q is the conclusion
biconditional operation
<->; p if and only if q; p iff q; only T if both are T or both are F
compound propositions are logically equivalent when
they have the same truth value; disregard individual/composing propositions
