30 points
>
Time management is very much important in IIT JAM. The eduncle test series for IIT JAM Mathematical Statistics helped me a lot in this portion. I am very thankful to the test series I bought from eduncle.
Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Biotechnology (BT)
What is the difference between sub set and proper sets
what is the difference between sub set and proper sets
2 Answer(s)
Answer Now
- 0 Likes
- 2 Comments
- 0 Shares
-
![comment-profile-img]()
>
Ujjawal vishal
![best-answer]()
A is subset of set B if every element of A is in B . Let B={1,2} then if A is subset of B then A can be phi, {1},{2},{1,2}...that means A set is subset of itself. But a proper subset of a set is not equal to itself. So, in same example, proper subsets of B are phi, {1},{2} only. Additionally, total no of subsets of a set having n elements=2^n while no of proper subsets =(2^n)-1 (excluding the set itself)
Do You Want Better RANK in Your Exam?
Start Your Preparations with Eduncle’s FREE Study Material
- Updated Syllabus, Paper Pattern & Full Exam Details
- Sample Theory of Most Important Topic
- Model Test Paper with Detailed Solutions
- Last 5 Years Question Papers & Answers
Sign Up to Download FREE Study Material Worth Rs. 500/-
Abhijeet Gaurav![best-answer]()
In set theory, a subset is a set containing some or all members of another set. For example, if the set S is defined as { a, b, c }, then { a }, { a, c } and { a, b, c } are all subsets of S. The symbol ⊆ is used to indicate a subset. So, if S is a subset of T, then S ⊆ T. The symbol is sometimes read as “subset or equal to”, but in general, sets that are equal are subsets of each other. The formal definition for a subset is: S ⊆ T ↔ ∀x(x∈S → x∈T) That is, S is a subset of T if and only if every element of S is also an element T. By definition, a set is simply a collection of elements. By definition, a set A is a subset of a set B if and only if every element in A is also in B. In other words, A⊆B iff x∈A implies x∈B. Note that every set is in fact a subset. Because, trivially, A⊆A for all sets A. In words, "every set is a subset of itself." Also, the empty set ∅ is a subset of every set A, because the empty set vacuously satisfies the definition of subset. In words, "the empty set is a subset of every set."