Subsets
If A and B are sets such that each element of A is an element of B, then we say that A is a subset of B and write A B. ..
If A and B are sets such that each element of A is an element of B, then we say that A is a subset of B and write A B. ..Some Results of Subsets
Some Results of Subsets..
Some Results of Subsets..Total number of subsets in a set is 2n
The total number of all possible subsets of a given set containing n elements is 2 ..
Note:
Set of real numbers is a proper subset of the set of Complex numbers..
or
A set A is said to be a proper subset of B if B contains at least one element, which is not in..
Proof:
r = (0, 1, 2, 3, . . . n) Hence the total number of subsets i..
r = (0, 1, 2, 3, . . . n) Hence the total number of subsets i..Complement of a set
Let U be a universal set, A be any subset of U, then the elements of U which are not in A i.e., U - A is the complement of A w.r.t. U is written as A' = U - A = A c ..
Let U be a universal set, A be any subset of U, then the elements of U which are not in A i.e., U - A is the complement of A w.r.t. U is written as A' = U - A = A c ..Proof:
The null set f is a subset of every set, in particular f A. By hypothesis, A f . The two conditions imply A = f..
Basic Definitions
: Two sets A and B are said to be equal if and only if they contain the same elements i.e. if every element of A is in B and every element of B is in A. We denote the equality by A = B. Cardinality of a Set A: The number of elements in a finite set A, is the cardinality of A and is denote..
Power Set
The family of all subsets of any set S is called the power set of S. We denote the power set of S by P (S). If a set S is finite, say S has n elements, then the power set of S can be shown to have 2 n elemen..
The family of all subsets of any set S is called the power set of S. We denote the power set of S by P (S). If a set S is finite, say S has n elements, then the power set of S can be shown to have 2 n elemen..See what our Users say :
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