The total number of subsets of a Finite Set containing n elements is 2ⁿ

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 ∈…

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…

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…

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…

Semi-Open or Semi-Closed interval If a and b are two real numbers such that a < b, then the sets (a, b] = { x : x ∈ R, a < x ≤ b}  and  [a, b)={ x ∈ R, a ≤ x < b  are known  as  semi-open  or  semi-closed intervals . (a,…