LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

SUBSET & SUPERSET

**Subset
& Superset**

**If A & B are two sets such that every elephant of A is an
elephant of B, we say that A is a subset of B or A is included in B. we express
this in symbols as A ⊆ B, If the set A is not a Subset
of the Set B, we write A ⊄ B**

**Let, A
= { 2, 3 }, and B = { 2, 3, 4, 5 },
then 2 ∈ A and 2 ∈ B,
also 3 ∈ A
and 3 ∈ B, hence every element of A is
an element of B. so, A ⊆ B. **

**However then 4 ∉ A and 4 ∈ B, also 5 ∉ A, and 5 ∈ B, so every element of B do not belong to or
not an element of A. So, B is not a subset of A, which is to mentioned like B ⊄ A.**

**Please reminder that, each set is a subset of itself, thus
for any set A, ****A ****⊆ ****A or for any set B, ****B ****⊆ ****B. **

**It has been considered that, the null set φ is or will be a ****subset**** of
every set.**

**In the examples we have considered,**

** 1) The number of
subsets of the set A = 4 = 2² = 2ⁿ (
where n number of elements of A )**

** 2) The number of subsets of the set B = 8 = 2ᶟ = 2ⁿ ( where
n number of elements of B )**

** 3) The number of
subsets of the set C = 16 = 2⁴ = 2ⁿ (
where n number of elements of B )**

**If the number of elements of a finite set X is n, the number
of the subsets of X = 2ⁿ**

**Proper
Subsets -**

**If the sets X & Y are such that, where every element of X is supposed to be an
element of Y but Y has at least one element which is not an element of X then
X is called a proper subset of Y, this is expressed in symbols as X ⊂ Y.**

**Super Set –**

**Let X be a subset of Y, i.e, X ⊆ Y, then
we say that B is a superset of A. We express this in symbols as Y ⊇ X**

**Example.-1) let X = { 3, 5, 7 } and Y = { 1, 2, 3, 4, 5, 6,
7, 8 }, then Y ⊇ X**

** **

**Equal Set –**

**Two sets X & Y are suppose to be equal if each element of X is an
element of Y and each element of Y is an element of X, in other words, The
Set X & Y are equal whenever X is a subset of Y and Y is a subset of X, that
is X ⊆ Y and Y ⊆ X. so we can conclude that, X & Y are equal set and the equal sets X & Y are denoted by X = Y. **

** **