Universal Set
Universal Set : A set containing all elements of a problem under consideration is called universal set . It is denoted by U .
E . g . While studying the system of numbers , we are interested in the set of natural numbers and its subsets such as the set of all prime numbers , the set of all even numbers , and so forth . This basic set is called the “ Universal Set ”. Here universal set is R .
Numerical : Recommend a universal set for A = { 1 , 3 , 5 } , B ={ 1,2,7 } Solution : Set B = { 1,2,3,4,5,6,7,8 ,} can be a universal set in this case
Open & Closed Intervals Let a , b ∈ R and a < b .
Open interval is denoted by ( a , b ) = { x : a < y < b }. Endpoints element NOT included .
Closed interval is denoted by [ a , b ] = { x : a ≤ x ≤ b }. Endpoints element included .
We can also have intervals closed at one end and open at the other , i . e ., o
o
[ a , b ) = { x : a ≤ x < b } is an open interval from a to b , including a but excluding
( a , b ] = { x : a < x ≤ b } is an open interval from a to b including b but excluding