REVIEW: Set Theory - Basics

Front

What is a set in mathematics?

Back

A set is a collection of distinct objects, considered as an object in its own right. For example, the set of natural numbers can be represented as S = {1, 2, 3, ...}.

Front

What does the symbol \( \in \) represent in set theory?

Back

The symbol \( \in \) means 'is an element of'. For example, if A = {1, 2, 3}, then 2 \( \in \) A.

Front

What does the symbol \( \subseteq \) mean?

Back

The symbol \( \subseteq \) means 'is a subset of'. A set A is a subset of set B if every element of A is also an element of B.

Front

What is the difference between a subset and a proper subset?

Back

A subset can be equal to the set, while a proper subset must contain at least one element that is not in the other set.

Front

What does the symbol \( \cup \) represent?

Back

The symbol \( \cup \) represents the union of two sets, which is the set of elements that are in either set or both.

Front

What does the symbol \( \cap \) represent?

Back

The symbol \( \cap \) represents the intersection of two sets, which is the set of elements that are common to both sets.

Front

What is the complement of a set?

Back

The complement of a set A refers to elements not in A, relative to a universal set U. It is denoted as A' or \( \bar{A} \).

Front

What is the empty set?

Back

The empty set, denoted as Ø, is a set that contains no elements.

Front

What does \( A - B \) represent?

Back

The expression \( A - B \) represents the difference between sets A and B, which includes elements in A that are not in B.

Front

If A = {1, 2, 3} and B = {2, 4, 6}, what is A \( \cap \) B?

Back

A \( \cap \) B = {2}, which is the set of elements common to both A and B.