Equal sets
Two sets A and B are said to be equal if they have exactly the same elements and we write A = B .
Otherwise , the sets are said to be unequal and we write A ≠ B .
Examples : Let A = { 1 , 2 , 3 , 4 } and B = { 3 , 1 , 4 , 2 }. Then A = B . Let C = { 1 , 2 , 3 , 4 } and D = { 1,2,3,5 }. Then C ≠ D .
If set A = { 1 , 2 , 3 } and B = { 2 , 2 , 1 , 3 , 3 }. Then A = B , since each element of A is in B and vice-versa . That is why we generally do not repeat any element in describing a set .
Sub sets
A set A is said to be a subset of a set B if every element of A is also an element of B .
Consider set A = set of all students in your class , B = set of all students in your School . We note that every element of A is also an element of B ; we say that A is a subset of B .
A is subset of B is expressed in symbols as A ⊂ B . The symbol ⊂ stands for ‘ is a subset of ’ or ‘ is contained in ’.
It follows from the above definition that every set A is a subset of itself , i . e . A ⊂ A .
Since the empty set φ has no elements , we agree to say that φ is a subset of every set .