Set theory

Front

What is a set?

Back

A set is a collection of distinct objects, considered as an object in its own right. For example, A = {1, 2, 3} is a set.

Front

What is the intersection of two sets A and B?

Back

The intersection of two sets A and B, denoted A ∩ B, is the set of elements that are common to both A and B.

Front

If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∩ B?

Back

A ∩ B = {2, 3}.

Front

What is the union of two sets A and B?

Back

The union of two sets A and B, denoted A ∪ B, is the set of all elements that are in A, in B, or in both.

Front

If A = {1, 2} and B = {2, 3}, what is A ∪ B?

Back

A ∪ B = {1, 2, 3}.

Front

What is the complement of a set A?

Back

The complement of a set A, denoted A', is the set of all elements in the universal set that are not in A.

Front

If the universal set U = {1, 2, 3, 4, 5} and A = {2, 3}, what is A'?

Back

A' = {1, 4, 5}.

Front

What is roster form in set notation?

Back

Roster form is a way of specifying a set by listing its elements within curly braces. For example, A = {1, 2, 3}.

Front

What is set-builder notation?

Back

Set-builder notation is a shorthand used to describe a set by stating the properties that its members must satisfy. For example, A = {x | x is an even number}.

Front

What does it mean for two sets to be equivalent?

Back

Two sets are equivalent if they have the same number of elements, regardless of whether the elements are the same.