It is defined as a subset which contains only the values which are contained in the main set, and atleast one value less than the main set. Total no of subsets of {a,b,c} = $2^3$ = 8. Solution: We can find a variety of examples of subsets in everyday life such as: Example 3: Find the number of subsets and the number of proper subsets for the given set A = {5, 6, 7, 8}. A proper subset is defined as a subset which contains only the values which are contained in the main set, and atleast one value less than the main set. PROPER SUBSET. (note that the null set ∅ is a subset of every set). The subsets of any set consisting of all possible sets including its elements and the null set. It means that X is contained in Y, If a set X is a subset of set Y, we can say that Y is a superset of X, The formula to calculate the number of subsets of a given set is 2, The formula to calculate the number of proper subsets of a given set is 2. But in proper subsets, if X is a subset of Y, if and only if every element of set X should present in set Y, but there is one or more than elements of set Y is not present in set X. 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Improper Subset: Because {1,2} is a subset but not a proper subset of {1,2}. Solution : The given set A contains 5 elements. A proper subset is one that contains few elements of the original set whereas an improper subset, contains every element of the original set along with the null set. Register with the BYJU’S – The Learning App today. Problem 1 : Let A = {1, 2, 3, 4, 5}. Solution: The subset of A containing no elements - { } But each set have two improper subset, so number of improper subsets are 6. If a set A is a collection of even number and set B consist of {2,4,6}, then B is said to be a subset of A, denoted by B⊆A and A is the superset of B. It is represented by P(A). Some of the important properties of subsets are: Example 1: How many number of subsets containing three elements can be formed from the set, Solution: Number of elements in the set = 10, Therefore, the number of possible subsets containing 3 elements = 10C3.

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