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…
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] = {…
Open interval If a and b are two real numbers such that a < b, then the set of all real numbers x satisfying a x b is called an open interval and is denoted by (a, b) or ]a, b[ . Thus, (a,b) = (x: x ∈ R, a < x < b).
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,…
Universal set In any discussion in set theory, there always happens to be a set that contains all sets under consideration i.e. it is a super set of each of the given sets. Such a set is called the universal set and is denoted by U. Thus a set that contains all sets in a…
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…
Venn diagrams The diagram drawn to represent sets are called Venn-diagram. In Venn-diagram the universal set U is represented by points within the rectangle and its subsets are represented points in closed curves (usually circles) within the rectangle. If a set A is a subset of a set B, then the circles representing A is…
Union of sets Let A and B be two sets. The union of A and B is the set of all those elements which belong either to A or to B or to both A and B. We denote A union B by notation “A ∪ B” Thus A∪B = { x : x ∈…
Intersection of sets Let A and B be two sets. The intersection of A and B is the set of all those elements that belongs to both A and B. See in Fig(v) shaded region show A∩B We denote A intersection B by notation “A ∩ B” Thus A∩B = { x : x ∈…
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,…
