What is Relation in Mathematics

Symmetry difference of sets Let A and B be two sets. The symmetry difference of sets A and B is the set (A-B) ∪ (B-A)  and it is denoted by A ∆ B. Then A∆B=(A-B) ∪ (B-A) = {x : x ∉ A ∩ B}. In Fig 9 shaded region represents A∆B Fig (9) Example…

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

First Law for a Closed System Undergoing a Quasi-static process In many occasions it is necessary to consider a system undergoing a process rather than a cycle. The equation, ∮ dQ − ∮ dW = 0 is applicable during the system undergoing a cycle, and algebraic sum of all energies transfer across the system boundary…

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…