∈ R, a ≤ x < b are known as semi-open or semi-closed intervals . (a, b] and [a , b) are also denoted by ]a, b] and [a, b[ respectively.
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…
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…
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 ∈…
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…
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…
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…
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…
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…
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 ∈…
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…
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…
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…
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…
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…
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