Closed Intervals | Set
CLOSED INTERVALS Let a and b be two given real numbers such that a < b. Then the set of all real numbers x such that a ≤ x ≤ b is called a closed interval and is denoted by [a, b] . Thus, [a, b] = { x : x ∈ R,…
The empty set is a subset of every set
THEOREM 2 The empty set is a subset of every set. PROOF Let A be any set and ϕ be the empty set.ln order to show that ϕ ⊆ A,we must show that every element of ϕ is an element of A also. But ϕ contains no element. So, every element of ϕ…
Every set is a subset of itself
THEOREM 1 Every set is a subset of itself. PROOF:- Let A be any set. Then, each element of A is clearly in A itself. Hence, A ⊆ A.
Improper subset | proper subset | Set | Subsets | super set
Subsets | Proper subset | Improper subset | Super set
SUBSETS Let A and B be two sets. If every element of A is an element of B, then A is called a subset of B and B is called super set of A. A ⊆ B is read as A is subset of B B ⊃ A is read as B is super set…
Closed intervals | Empty set | equal sets | Equivalent sets | Finite and infinite set | Set | Singleton set | Types of sets
Types of sets
TYPES OF SETS a) Empty setA set is said to be empty or null or void set if it has no element and it is denoted by Φ In Roster method is Φ denoted by { }.Example{ x : x ∈ R, x2=-2 }=Φ { x : x ∈ N, 5<x<6 }=Φ D={ x :…
Representation of set | Roster or Tabular form | Set Builder form
REPRESENTATION OF A SET A set is often described in the following two forms. One can make use of any one of these two ways according to his/her convenience (i) Roster form or Tabular form(ii) Set-builder formLet us now discuss one by one.(i) Roster form or Tabular form:-In this form a set is described by…
What is a set | Set theory
What is a set? Set can be defined as the collection of well-defined object that’s all.The meaning of ” well-defined” in set is those type of collection which is not depend on choice.Like collection of beautiful women in India. Which depend on choice only and different people has different different choice. So such collection is…