Set Theory & Logic Vocabulary

a collection of distinct objects considered as a whole

“The set of prime numbers less than 10 is {2, 3, 5, 7}.”

a set whose elements are all contained in another set

“The even numbers are a subset of the integers.”

the set containing all elements from two or more sets

“The union of {1,2} and {2,3} is {1,2,3}.”

the set of elements common to two or more sets

“The intersection of {1,2,3} and {2,3,4} is {2,3}.”

the number of elements in a set

“The cardinality of {a, b, c} is 3.”

a one-to-one correspondence between two sets

“A bijection proves two sets have equal cardinality.”

a statement containing variables that becomes true or false when values are assigned

“The predicate 'x is even' is true when x = 4.”

a symbol specifying the quantity of specimens in a domain

“The universal quantifier ∀ means 'for all'.”

a statement that is true under all possible interpretations

“'It will rain or it will not rain' is a tautology.”

a statement that contradicts itself or defies intuition

“Russell's paradox shook the foundations of set theory.”