people liked products A and B, people liked products C and A, people liked products B and C and liked all the three products. Find how many liked product C only. Summary 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 . ® A power set of a set A is collection of all subsets of A. It is denoted by P(A). MATHEMATICS ® 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) Historical Note The modern theory of sets is considered