# CLASS-7SUBSET OF FRACTION

Subsets

If two sets X & Y, where every member of ‘X’ is also a member of ‘Y’ then we can say that, ‘X’ is a subset of ‘Y’ then this is to be written like X Y, the set ‘X’ is a subset of ‘Y’ can also be expressed by saying ‘Y’ is a superset of ‘X’, we can write like Y X.

Example- 1

Let, X = { 3, 5, 6, 7 }, Y = { 3, 4, 5, 6, 7 }, Z = { 1, 2, 4, 8, 9 }

3 ϵ X  &  3 ϵ Y ;  5 ϵ X  &  5 ϵ Y ;  6 ϵ X  &  6 ϵ Y ;  7 ϵ X  &  7 ϵ Y ; whereas  4 X  but  4 ϵ Y,

So, we can see that X Y and also, Y X

And,  3 ϵ X but 3 Z,  5 ϵ X but 5 Z, 6 ϵ X but 6 Z,  7 ϵ X but 7 Z, whereas

1 X  but  1 ϵ Z ;  2 X  but  2 ϵ Z ;  4 X  but  4 ϵ Z ; 8 X  but  8 ϵ Z ; 9 X  but  9 ϵ Z

So, we can see that X Z

Also, 3 ϵ Y but 3 Z  ; 4 ϵ Y but 4 Z  ; 5 ϵ Y but 5 Z  ; 6 ϵ Y but 6 Z ; 7 ϵ Y but 7 Z, where as

1 Y  but  1 ϵ Z  ; 2 Y  but  2 ϵ Z ; 4 Y  but  4 ϵ Z  ; 8 Y  but  8 ϵ Z  ; 9 Y  but  9 ϵ Z ;

So, we can see that Y Z

Example – 2

Let, A = { y / y is a letter of the word BISWADEEP }

And  B = { y / y is a letter of the word BISWA } , then prove that  B    A.

Ans.)  A = { B, I, S, W, A, D, E, P }  and  B = { B, I, S, W, A }

You can see from above that, members of Set ‘B’ belongs to members of Set ‘A’

So, it’s proven that  A.

Example – 3

Write all the subset of the sets of the set { 0, 2, 4, 5, 6 }

Ans.) There are five numbers in { 0, 2, 4, 5, 6 }, so subset of one members each will be {0}, {2}, {4}, {5}, {6}.

The subsets of two members each will be {0,2}, {0,4}, {0,5}, {0,6}, {2,4}, {2,5}, {2,6}, {4,5}, {4,6}, {5,6}.

Also, it has been considered that, the empty set φ and the set itself are two subsets of the set, the required subset are φ, {0}, {2}, {4}, {5}, {6}, {0,2}, {0,4}, {0,5}, {0,6}, {2,4}, {2,5}, {2,6}, {4,5}, {4,6}, {5,6}.