Set theory

How to denote a set?

To denote a set use { }

What does A ∪ B represent in set theory?

Union - Elements that belong to set A or set B.

What does A ∩ B represent?

Intersection - Elements that belong to both sets A and B.

What does A ⊄ B signify in set notation?

Left set is not a subset of the right set.

What is a proper subset (A ⊂ B)?

Subset has fewer elements than the set.

What does A ⊃ B indicate?

Proper superset - Set A has more elements than set B.

What is meant by a superset (A ⊇ B)?

Set A has more elements or equal to the set B.

What does an empty set Ø represent?

A set that contains no elements.

What is a power set P(C)?

All subsets of set C.

What does A \ B or A-B represent in set notation?

Relative complement - objects that belong to A and not to B.

What is cardinality |B| of a set.

The number of elements in set B.

What does A × B represent in set theory?

Cartesian product - set of all ordered pairs from A and B.

What are natural numbers without zero?

N1 = {1, 2, 3, 4, 5,…}.

What set of numbers does Q symbol represent?

The set of rational numbers.

What set of numbers does Z symbol represent?

Set of integers: Z = {…-3, -2, -1, 0, 1, 2, 3,…}.

What is the definition of complex numbers C?

C = {a + bi | a, b ∈ R, i = √(-1)}

What is the definition of real numbers R?

R = {x | -∞ < x < ∞}.

What is a subset?

A set A is a subset of set B if every element of A is also an element of B.

What is a superset?

A set B is a superset of set A if it contains every element of A, meaning all elements of A are also elements of B.

What is a set?

In mathematics, a set is a collection of distinct objects, considered as an object in its own right. These objects can be anything: numbers, letters, symbols, or even other sets. The elements of a set are usually denoted by curly braces {}.

What is an ordered pair?

An ordered pair in mathematics is a pair of elements where the order of the elements is significant. It is typically written in the form ( (a, b) ), where ( a ) is the first element and ( b ) is the second element.

The key characteristic of an ordered pair is that ( (a, b) ) is different from ( (b, a) ) unless ( a ) and ( b ) are the same. For example, ( (2, 3) ) is not the same as ( (3, 2) ).