Difference of Sets
Difference of sets
Fig (vii) |
Fig (viii) |
Fig (vii) |
Fig (viii) |
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,…
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…
Thermodynamic system Thermodynamic system is defined as quantity of matter or a region in a space chosen for study. Everything external to the system is called surroundings. The system is separated from the surroundings by the boundary that may be real or imaginary The boundary does not intervene between the system and surroundings. It only…
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…
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…
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…