Sets

tttttt....A set is a well-defined collection of objects. There are two methods of representing a set: (i) Roster or tabular form (ii) Set-builder form. A set which does not contain any element is called the empty set or the null set. A set which is empty or consists of a definite number of elements is called finite set. Two sets A and B are said to be equal if they have exactly the same elements. A set A is said to be a subset of a set B if every element of A is also an element of B. A singleton set has only one element. The collection of all subsets of a set A is called the power set of A. The universal set is usually denoted by U and all its subsets by the letters A, B, C, etc. The union of two sets A and B is the set C which consists of all those elements which are either in A or in B. The intersection of two sets A and B is the set of all those elements which belong to both A and B. The difference of the sets A and B in this order is the set of elements which belong to A but not to B. Symbolically, it is written as A – B and read as “ A minus B”. The complement A′ of a set A can be represented by a Venn diagram.

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