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