Open Interval

Domain of relation Let R be a relation from a set A to a set B. Then the of all first components or coordinates of the ordered pairs belonging to R is called the domain of R. Thus, domain of R = { a : (a, b) ∈ R} Clearly, domain of R ⊆  A…

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,…

Energy interaction (Transition)             An energy interaction or transition is said to occur or to exist between two systems when one system influences a sustains the state of the other system. Thermodynamics mainly studies the interactions between heat and work and associated property change of the system In otherwords Energy…

Quasi-static process  A process during which the system remains nearly close to an equilibrium state is called Quasistatic process. In other words departure of the state of a system from Thermodynamic Equilibrium state will be Infinitesimally small. Quasi-static process Consider a system as shown in figure the system initially is in equilibrium state as weights…

Theorem 3          The total number of subsets of a finite set containing n elements is 2ⁿ.    Proof    Let A be a finite set containing n elements.Let 0 ≤ r ≤ n. Consider those subset,of A that  have r elements each.We know that the number of ways in which r elements can be chosen…

Complement of a set Let U be the universal set and let A be a set such that A ⊂ U. Then the complement of A with respect to U is denoted by A’ or Ac or U-A and is defined the set of all those elements of U which are not in A. Thus…