Pressure The molecules of a gas are in random motion. The rapidly moving molecules continually impact on the surface of the container and its effect is to produce a force over the surface. The force normal to unit area of surface is called pressure acting on the surface. The normal force exerted by the atmosphere…
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…
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…
Energy in a state Stored energy is the energy possessed by a system. Stored energy in the system is called energy in a state. It is associated with a state. It change depends only on the end states of the process and not on the path of…
Theorem 3 The total number of subsets of a finite set containing n elements is 2ⁿ. Proof Let A be a finite set containing n elements.Let 0 ≤ r ≤ n. Consider those subset,of A that have r elements each.We know that the number of ways in which r elements can be chosen…
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,…
