Paper 4: Fundamentals of Business Mathematics & Statistic

2.6 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

Two sets A and B are said to be disjoint if their intersection is empty, i.e., no element of A belongs

to B.

e.g. : ∴ A = {1,3, 5}, B = {2, 4},

A ∩ B = φ. Hence, A and B are disjoint sets.

Difference of two sets

If A and B are two sets, then the set containing all those elements of A which do not belong to B, is known

as difference of two sets, and is denoted by the symbol A ~ B or A – B (read A difference B).

Now, A ~ B is said to be obtained by subtracting B from A.

In symbols, A ~ B = {x ; x ∈ A and x ∉ B},

As for example :

(i) If A = {1, 2, 3 , 4, 5}

B = { 3, 5, 6, 7}, then A ~ B = {1, 2, 4}

(ii) If A = {x : x is an integer and 1 ≤ x ≤ 12}, B = {x : x is an integer and 7 ≤ x ≤ 14}

then A ~ B = {x : x is an integer and 1 ≤ x ≤ 6},

A ~ B is represented by a Venn diagram as above :-

The shaded portion represents A ~ B.

Complement of a Set :

Let U be the universal set and A be its sub-set. Then the complement set of A in relation to U is that set

whose elements belong to U and not to A.

This is denoted By A ́ (= U ~ A) or A ́ or A.

In symbols, A ́ = {x :A ∈ U and x ∉ A}.

We may also write : A ́ = {x : x ∉ A}.

Remarks :