Universal Set

A universal set is the set of elements from which elements may be chosen to form sets for a particular discussion. Thus the set of even numbers is a subset of the universal set of whole numbers. We denote a universal set by the symbol ξ or U or E. In this book as per notation specified in the syllabus, the universal set will be denoted by the symbol ξ. The universal set may change from problem to problem. For example, the set of letters of the alphabet is the universal set from which the letters of any word may be chosen to form a set.

For Example -

(i) In plane geometry, the universal set consists of all the points in a plane.

(ii) For the set of prime numbers, composite numbers, positive odd numbers and positive even numbers the universal set can be taken as the set of natural numbers.

(iii) For the set of players of football eleven of your school, the universal set may be taken as the set of pupils of your school.

(iv) Suppose we have to solve the in equation {x ǀ x < 5, x ∈ W}. The solution will be {0, 1, 2, 3, 4}. If universal set were the set of integers, i.e., {x ǀ x < 5, x ∈ Z} then the solution would be {………., -3, -2, -1, 0, 1, 2, 3,……………}. It will be an infinite set..

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