CBSE Class 11 Maths Notes: Sets – Set and Complimentary Set

UNIVERSAL SET

A non-empty set of which all the sets under consideration are subsets is called the universal set. In any application of set theory, all the sets under consideration will likely to be subsets of a fixed set called Universal Set. As name implies it is the set with collection of all the elements and usually denoted by ‘U’.

e.g. ≤ 1) set of real numbers R is a universal set for the operations related to real numbers.

COMPLEMENTARY SET

The complement of a set A with respect to the Universal Set U is difference of U and A. Complement of set A is denoted by  ≤ or A^C) ≤ or A¢). Thus  is the set of all the elements of the Universal Set which do not belong to the set A.

 = U – A = {x: x ∈ U and x ∉ A}

we can say that A ∪  = U ≤ Universal Set) and A ∩  = ϕ ≤ Void Set)

Some of the useful properties/operations on sets are as follows:

• A ∪ U = U
• A ∩ ϕ = ϕ
• ϕ^C = U
• U^C = ϕ

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