Laws of algebra of set THEOREM 1 (Idempotent Laws) For any set A (i) A ∪ A = A (ii) A ∩ A = A PROOF (i) A ∪ A= { x : x ∈ A or x ∈ A} ={x : x ∈ A} = A (ii) A ∩ A = {x : x…
Introduction about thermodynamics Energy is the capacity to do work energy cannot be created or destroyed but only can be changed into other forms (principle of conservation of energy). Thermodynamics mainly deals with interaction between heat and work (mechanical energy) and change in the property is associated with these interactions. The interaction between heat and…
Difference of sets Let A and B be two sets. The difference of A and B written as A – B, is the set of all those elements of A which do not belong to set B Thus A – B={ x : x ∈ A and x ∉ B} or A – B={ x…
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…
Complement of a set Let U be the universal set and let A be a set such that A ⊂ U. Then the complement of A with respect to U is denoted by A’ or Ac or U-A and is defined the set of all those elements of U which are not in A. Thus…
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…
