Every set has a proper subset...........is it true? give reason
A subset A if a set B is called a proper subset of B if A ≠ B. Every set is a subset of itself and the empty set is subset of every set. These two subsets are called improper subsets.
Consider a set having n elements.
Total number of subsets of the finite set = 2n
∴ Total number of proper subsets of the finite set = 2n – 2
Singleton set is a set consisting of a single element.
Number of proper subset of a singleton set = 21 – 2 = 0
∴ Singleton set has no proper subset.
Thus, every set does not have a proper subset.