UPSC NDA I 2021 Mathematics Solved Paper

Concept
1. The null set is a subset of every set. (φ⊂eqA )
2. Every set is a subset of itself. (A⊂eqA )
3. The number of subsets of a set with n elements is 2n.
‌ Explanation: ‌
1. The null set is a subset of every set - The intersection of two sets is a subset of each of the original sets.
So if {} is the empty set and A is any set then{} intersect A is {} which means Z{} is a subset of A and {} is a subset of{} . You can prove it by contradiction. Let's say that you have the empty set {} and a set A.
2. Every set is a subset of itself. (A⊂eqA )
3. If n=10 then 210=1024
So, all three statements are true.