CBSE Class 11-science Answered

A set A is a subset of a set B if A is "contained" inside B. Notice that A and B may coincide. The relationship of one set being a subset of another is called inclusion.

If A and B are sets and every element of A is also an element of B, then:

• A is a subset of (or is included in) B, denoted by ,

or equivalently

• B is a superset of (or includes) A, denoted by

If A is a subset of B, but A is not equal to B (i.e. there exists at least one element of B not contained in A), then

• A is also a proper (or strict) subset of B; this is written as

The empty set is the unique set having no (zero) members. Some axiomatic set theories assure that the empty set exists by including an axiom of empty set; in other theories, its existence can be deduced. Many possible properties of sets are trivially true for the empty set.