∈ 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…
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 ∈…
Types of relation Void relation:- Let A be a set. Then, Φ ⊆ A x A and so it is a relation on A. This relation is called the void or empty relation on set A. In other words, a relation R on a set A is called void or empty relation, if no element…
Function as a set of ordered pairs Let A and B be two non-empty sets. A relation f from A to B i.e a subset of A × B is called a function (or a mapping or a map) from A to B, if i) for each a ∈ A there exists b ∈ B…
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…
Conservation of Energy In the early part of 19th century the scientist developed the concept of energy and hypothesis that it can be neither created nor destroyed ; this come to be known as the law of the conservation of energy. The first law of thermodynamics is merely one statement of this…
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