Ordered Pairs and Equality of an Ordered Pairs

Power set  Let A be a set. Then the collection or family of all subsets of A is called the power set of A and is denoted by P(A). That is.  P(A) = { S : S ⊂ A }. Since the empty set and the set A itself are subsets of A and are…

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…

Introduction about thermodynamics Energy is the capacity to do work energy cannot be created or destroyed but only can be changed into other forms (principle of conservation of energy). Thermodynamics mainly deals with interaction between heat and work (mechanical energy) and change in the property is associated with these interactions. The interaction between heat and…

Intervals as subsets of R    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] = {…

Power set  Let A be a set. Then the collection or family of all subsets of A is called the power set of A and is denoted by P(A). That is.  P(A) = { S : S ⊂ A }. Since the empty set and the set A itself are subsets of A and are…

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…