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.

  • 1
What are you looking for?