LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

SUBSETS

**SUBSETS –**

**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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