What is Relation in Mathematics

Thermodynamic equilibrium Thermodynamic state is a condition of a system and is specified by its thermodynamic properties. Thermodynamic Equilibrium of a system is a state such that if the system is isolated from its surroundings no change in thermodynamic properties would occur. A system will be in a state of thermodynamic equilibrium if the conditions…

Subsets of the set R of real numbers Following sets are important subsets of the set R of all real numbers:        (i)  The set of all natural numbers N = { 1, 2, 3, 4, 5, 6,…. }      (u)  The set of all integers Z =  { … – 3, – 2, -1,…

Laws of algebra of set THEOREM 1 (Idempotent Laws) For any set A (i) A ∪ A = A (ii) A ∩ A = A PROOF  (i) A ∪ A= { x : x ∈ A or x ∈ A} ={x : x ∈ A} = A    (ii) A ∩ A = {x : x…

Semi-Open or Semi-Closed interval If a and b are two real numbers such that a < b, then the sets (a, b] = { x : x ∈ R, a < x ≤ b}  and  [a, b)={ x 😡 ∈ R, a ≤ x < b  are known  as  semi-open  or  semi-closed intervals . (a,…

Disjoint sets Two sets A and B are said to be disjoint, if A∩B=Φ. If A∩B≠Φ, then A and B are said to be intersecting or overlapping sets As shown in Fig(vi) Fig(vi)  Example If A={ 1, 2, 3, 4, 5, 6 }, B={ 7, 8, 9, 10, 11 } and C= { 6, 8, 10,…

Function as a set of ordered pairs     Let  A and B be two non-empty sets. A relation f from A to B i.e   a subset of A × B is called a function (or a mapping or a map) from A to B, if i) for each a ∈ A there  exists b ∈ B…