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# local_media1464210615735785759.pptx

Mathematics in the Modern World

Mathematics in the Modern World

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### local_media1464210615735785759.pptx

1. 1. LET'S LEARN!
2. 2. A set is a collection of well-defined objects that contains no duplicates. The objects in the set are called the elements of the set. To describe a set, we use braces { }, and use capital letters to represent it. What is a set?
3. 3. Types of Sets 1. Finite and infinite set 2. Empty set 3. Singleton set 4. Equal sets 5. Equivalent sets 6. Universal set 7. Subsets(proper and improper) 8. Power set
4. 4. Finite and Infinite Set Examples: 1. Set A = {2,4,6,8,10} — finite set 2. Set B = {1,3,5,7,9…} — infinite set A finite set contains elements that can be counted and terminates at certain natural number. While the infinite set whose elements can't be estimated, but has some figure or number, which is large to precise in a set.
5. 5. Empty Set The empty set, or null set, ∅ or { }, which has no members/elements at all. Example: Set C = { }
6. 6. Singleton Set ("Singleton of a") Example: Set D = {10} A set with only one member is called a singleton or a singleton set.
7. 7. Equal Sets Two sets are equal if they contain exactly the same elements. Example: {2,4,6,8} = {2,4,6,8}
8. 8. Equivalent Sets Examples: 1. {a, b, c}, {1,2,3} 2. {1,4,3}, {2,5,4} Two sets are equivalent if they contain the same number of elements.
9. 9. Universal Set A set that contains all the elements considered in a particular situation and denoted by U. Example: a. Suppose we list the digits only. Then, U = {0,1,2,3,4,5,6,7,8,9}, since U includes all the digits. b. Suppose we consider the whole numbers. Then, U ={0,1,2,3,…} since U contains all whole numbers.
10. 10. Subsets Examples: 1. A = {7,9} is a subset of B = {6,9,7} 2. D = {10,8,6} is a subset of G = {10,8,6} A set A is called a subset of set B if every element of A is also an element of B. "A is a subset of B is written as A ⊂ B. A proper subset is a subset that is not equal to the original set, while the improper subset is opposite of it. Example: Given {3,5,7} then the proper subset are { }, {5,7}, {3,5}, {3,7}. The improper subset is {3,5,7}.
11. 11. Power Set It is the family of all the subsets of A denoted by Power (A). Example: Given set A = {x, y}, the Power (A) = {∅, {x}, {y}, {x, y} or {x|x is a subset of A.
12. 12. THANK YOU