Reading is to the mind, as exercise is to the body. – Brian Tracy
This chapter deals with some basic definitions and operations involving sets. These are summarised below:
A set is a well-defined collection of objects.
A set which does not contain any element is called empty set.
A set which consists of a definite number of elements is called finite set, otherwise, the set is called infinite 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 subset of a set B, if every element of A is also an element of B. Intervals are subsets of R.
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A power set of a set A is collection of all subsets of A. It is denoted by P(A).
The union of two sets A and B is the set 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 elements which are common. The difference of two sets A and B in this order is the set of elements which belong to A but not to B.
The complement of a subset A of universal set U is the set of all elements of U which are not the elements of A.
For any two sets A and B, (A ∪ B)′ = A′ ∩ B′ and ( A ∩ B )′ = A′ ∪ B′
If A and B are finite sets such that A ∩ B = φ, then n (A ∪ B) = n (A) + n (B). If A ∩ B ≠ φ, then n (A ∪ B) = n (A) + n (B) – n (A ∩ B)