Isha posted an Question
April 22, 2020 • 14:48 pm 30 points
  • IIT JAM
  • Biotechnology (BT)

What is the difference between sub set and proper sets

what is the difference between sub set and proper sets

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  • 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."

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    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)

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