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A set is said to be a finite set if either it is empty or it contains a finite number of elements; otherwise, it is said to be an infinite set. Infinite sets are classified into two types:
(1) Denumerable and
An infinite set is said to be denumerable if the properties defining the set allow one to arrange its elements in the form of a sequence.
(2) Non- denumerable.
On the contrary, an infinite set is said to be non- denumerable if the properties defining the set do not allow one to arrange its elements in the form of a sequence.
Countable and Uncountable Sets
A set is said to be countable if it is finite or denumerable. A non-denumerable is also called uncountable set.
Equal Sets
Two sets A and B are said to be equal (expressed by A = B) if A⊂B and B⊂A. Two equal sets contain precisely the same elements.
Incomparable Sets
There exist sets A and B such that neither A⊂B nor B⊂A. Such a pair of sets is said to be incomparable.
Universal Set
The subsets of a single fixed set called the universal set in relation to its subsets. A universal set is generally denoted by U. Let U be the universal set and A, B, C,. ..... be the subsets of U.
Disjoint Sets
Two subsets A and B are said to be disjoint if A∩B=∅.
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