Sets whose all elements are contained in another set Y are called subsets of the set Y. For example if A = {1, 3, 5, 7, 9, 11} and B = {3, 9}, the B is the subset of A.

Definition  If A & B are sets such that every member of set A is a member of set B, then set A is called a subset of set B.

Since, by definition, if A = {x, y, z}, and B = {x, y, z} then A is a subset of B. also since A is equal to B, we use the symbol for “is a subset of”. Thus, A ⊆ B, the symbol means contained in or possibly equal to.

Proper Subset

If a set Q = {a, c} is a subset of set P = {a, b, c, d} and set Q is not equal to set P, then set Q is called a proper subset of set P and is expressed as Q ⊂ P. The set P is called the superset of set Q. It is expressed as P ⊃ Q.

The symbol indicates is not a subset of and the symbol indicates is not a proper subset of.

   -  is a subset of

   -  is a proper subset of

  -  is not a proper subset of

   -  is a super-set of

Some Theorem On Subsets

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