Subset :A {a,b} is a set. By the elements of set A, the sets {a,b}, {a},{b} can
be formed. Again, by not taking any element φ set can be formed.
Here, each of {a,b}, {a},{b},φ is subset of set A.
So, the number of sets which can be formed from any set is called subset of that set.
The sign of subset is . If Bis the subset of A, it is read as BA.B is a subset
of A. From the above subsets, {a,b} set is equal to A.
? Each set is the subset of itself.
Again, from any set, φ set can be formed.
? φ is a subset of any set.
Q { 1 , 2 , 3 } and R { 1 , 3 } are two subsets of P { 1 , 2 , 3 }. Again P Q?QP and RP.
Proper Subset :
If the number of elements of any subset formed from a set is less than the given set,
it is called the proper subset. For example : A { 3 , 4 , 5 , 6 } and B { 3 , 5 } `are two
sets. Here, all the elements of B exist in set A.? BA
Again, the number of elements of B is less then the number of elements of A.
? B is a proper subset of A and expressed as BA.
Example 5. Write the subsets of P {x,y,z} and find the proper subset from the
subsets.
Solution : Given, P {x,y,z}
Subsets of P are {x,y,z},{x,y},{x,z},{y,z},{x},{y},{z},φ.
Proper subsets of P are {x,y},{x,z},{y,z},{x},{y},{z}
Equivalent Set :
If the elements of two or more sets are the same, they are called equivalent sets. Such
as,A { 3 , 5 , 7 } and B { 5 , 3 , 7 } are two equal sets and written as A B.
Again, if A { 3 , 5 , 7 }, B { 5 , 3 , 3 , 7 } and C { 7 , 7 , 3 , 5 , 5 }, the sets A,B and C
are equivalent. That is, A B C