Részhalmazviszony

Részhalmazviszony refers to the relationship between sets where one set is contained entirely within another. In set theory, a set A is considered a subset of a set B if every element that belongs to set A also belongs to set B. This relationship is denoted by the symbol $\subseteq$. Therefore, A $\subseteq$ B means that A is a subset of B.

If set A is a subset of set B, and set A is not equal to set B, then A is called a proper subset of B. This is denoted by the symbol $\subset$. So, A $\subset$ B implies that A is a subset of B, and there is at least one element in B that is not in A.

The concept of a subset is fundamental in mathematics and forms the basis for many other set-theoretic operations and definitions. For example, the intersection of two sets A and B is the set of all elements that are in both A and B. If A is a subset of B, then the intersection of A and B is simply A.

Conversely, if A is a subset of B, then B is said to be a superset of A, denoted by the symbol $\supseteq$ or $\supset$ for a proper superset. This means that B contains all the elements of A, and possibly more.

The empty set, denoted by $\emptyset$ or {}, is a subset of every set. This is because there are no elements in the empty set that are not in any other set. A set is always a subset of itself.