Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Revision for Sets: See Chapter 2.1, 2.2, 2.3 and 2.4 Sets (Pages 70 -78) Set: A collection of objects, ideas or numbers that can be clearly defined. Elements: ∈ The objects, ideas or numbers that are members of the set. ∉ Denotes that the object etc. is not an element within the set Braces: { } - Used to enclose the elements of a set e.g. {a,e,i,o,u}. Roster form of a set is written e.g. A = {a,e,i,o,u} Elipses: … indicates elements of a set not written: e.g. {1,2,3 …10} finite set {1,2,3 …} infinite set Set builder notation: describes what the set is in a simpler form, using a vertical line (|) to stand for ‘such that’. e.g. A = {𝓍 | 𝓍 is an even counting number} see Page 73/74. Empty or null set: { } or ∅ represents a set with no elements. ( NB. it is not written {∅}). Subsets (Pages 78 – 82): Subset: A ⊆ B Given any two sets A and B, if every element in A is also an element in B, then A is a subset of B. This includes the subset of the set itself. Proper subset: A ⊂ B – If A is a subset of B and there is at least one element of B that is not contained in A, the A is a proper subset of B. How to find the number of subsets: If a set contains n elements, then if contains 2n subsets. How to find the number of proper subsets: If a set contains n elements, then if contains 2n -1 proper subsets. Universal Set: Is the set that contains everything we are interested in now in a given problem and is denoted by U. Complement: This is everything in the universal set U but not in set A. The symbol for the complement is A’. Set Operations (Pages 82 – 86) Intersection: A ⋂ B If there are two dets A and B, then the intersection of A and B is the set of elements that are members of both A and B. Union: A ⋃ B If there are two sets A and B, then the Union of A and B is the total set of elements from both A and B. Know how to calculate (A ⋂ B)’ (A ⋂ B) ⋃ C within the parenthesis (brackets) first. A’ ⋃ B’ (A ⋃ B)’ etc. Remember to calculate operation Set builder notation Know the definition of intersection and union of two sets in set builder notation. **PRACTICE THE EXAMPLES AND EXERCISES FROM THE TEXT BOOK**