Disjoint Sets

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,…

Function as a machine A function can also be regarded as a machine that gives unique output in set B corresponding to each input from the set A just as the function ‘machine’ shown in Fig. 2(b). Which generate an output  y = 2×3 + 5 for each input x. Fig. 2(b)          Usually real…

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…

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…

Reversible and Irreversible processes           A process which can be reversible i.e., operated in opposite direction from any state during the process such that the system returns to its initial state and their may be no effect on the surroundings. Thus at the end of the process both the system and…