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}.”

Origin: From Old English settan `to cause to sit`

a set whose elements are all contained in another set

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

Origin: sub- `under` + set

the set containing all elements from two or more sets

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

Origin: Latin unio `oneness, unity`, from unus `one`

the set of elements common to two or more sets

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

Origin: Latin intersectio, from inter `between` + secare `to cut`

the number of elements in a set

“The cardinality of {a, b, c} is 3.”

Origin: Latin cardinalis `principal`, from cardo `hinge`

a one-to-one correspondence between two sets

“A bijection proves two sets have equal cardinality.”

Origin: Latin bi- `two` + French jection from Latin jacere `to throw`

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

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

Origin: Latin praedicatum `something declared`, from praedicare `to proclaim`

a symbol specifying the quantity of specimens in a domain

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

Origin: Latin quantus `how much` + -ifier

a statement that is true under all possible interpretations

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

Origin: Greek tautologia `repetition`, from tauto `the same` + logos `word`

a statement that contradicts itself or defies intuition

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

Origin: Greek paradoxon `contrary to expectation`, from para `contrary to` + doxa `opinion`