Fundamentals Tips

       FUNDAMENTALS TIPS

• A well defined collection of objects is said to be a set. Generally, set are denoted by capital letter A, B, C, …… and their elements by small letters a, b, c, ……….. The elements or members of a set are enclosed in the braces, {……}. e.g.: N = {1, 2, 3, 4, 5, ….…..}
• A set with fixed number of elements is said to be a finite set. e.g.: 
  A = {a, b, c} and B = {x : x is a month of a year}
• A set with not fixed number of elements is said to be an infinite set.
  e. g.: A = {x: x is an odd number}
• A set with no element is said to be a null set or empty set or void set. It is denoted by ɸ (phi) or { }. e.g.: A = { x : x is a man of height 8 meters}
• A set with only one element is said to be a singleton or unit set.
  e.g.: A = { x : x is a highest mountain in the world }
• The union of two or more sets is made just by grouping their elements together. In the case of overlapping sets, the common elements are mentioned only once while making the union.
• The intersection of sets A and B is the set that contains the elements
  common to A and B. e.g. A∩B = { x: x ∈ A and x ∈ B}
• The difference of sets A and B is the set of the elements of A which do
  not belong to B. e.g. A – B = {x : x ∈ A, but x ∈ B}
• If A be a subset of a universal set U, then the complement of A is the set of the elements of U which do not belong to A. e.g.:
  U = {1, 2, 3, 4, 5, 6, 7}
  A = {2, 3, 5}
  ∴ A = {1, 4, 6, 7}
• n(A∪B) = n(A)+n(B) [if A and B are the two disjoint sets]
• n(A∪B) = n(A)+n(B)-n(A∩B) [if A and B are Overlapping Sets]
• n(A∪B) = no(A) + no(B) + n(A∩B) [if no(A) and no(B) is given]
• n(A∪B∪C) = n(A)+n(B)+n(C)-n(A∩B)-n(B∩C)-n(A∩C)+n(A∩B∩C)
  [if A, B, C are Overlapping Sets]