Subsets( super set/ total subset/ proper subset)

 Subsets

1) Subsets 

=> A set 'A' is called as subset of 'B' if and only if all elements of 'A' are in 'B'.

    If 'A' is a subset of 'B', then 'B' is called as superset of 'A'.

   Symbol of superset => B ⊇ A

*** there is a mistake in the picture, null set is a proper subset of every set.

** This is read as, for every a that belongs to X if a belongs to Y too, then X is a subset of Y

2) Proper Subsets 

=> Proper Subset =( Total number of subsets - 1)  (or 2^n -1)

for example in the above example the total subset is 8 , therefore proper subset is = 8-1 i,e 7.

3) Finding total number of subsets with the formula 2ⁿ

=> If A is a set ,then the total number of subsets of A = 2ⁿ⁽ᴬ⁾

4) Some notes on subsets