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
Math 211 Sets 2012 J Candice Casey Amanda Ashley W. Kelly Taylor Tammy! Ethan Ronnie A C Ronni Jenny Candice Casey Amanda Ashley W. Taylor Tammy! Ethan Ronnie Scott Jenny S Tammy! Amanda G Taylor Candice Tammy! Casey Kelly Ashley W. Ashley H. Ethan Ronni T E Amanda Ashley W. Ethan Candice Casey Jenny Ashley H. Taylor Kelly Scott Tammy! N Tammy! Ethan Jenny P Candice Taylor Tammy! Kelly Ashley W. Amanda Ashley H. Scott M Candice Amanda Ashley W. Ethan Ronni Jenny H Candice Casey Amanda Kelly Ashley W. Ronni D Candice Casey Ashley H. Amanda Ethan Taylor Kelly Ashley W. Scott Jenny R Candice Casey Amanda Taylor Kelly Ashley W. Ashley H. Scott Ronni Jenny L Ashley H. Candice Casey Taylor Kelly Ashley W. Amanda Ethan Scott Ronni Jenny U Amanda Ashley H. Ashley J. Ashley W. Candice Casey Ethan Jenny Kelly Ronni Scott Tammy! Taylor Use your sets to learn the terminology and symbols we use for sets. This is called “set algebra.” (1) True or false. If false, write another statement using the same symbol, but different sets, that is true. (1) N ∈ E ____ (2) N ⊆ E ____ (3) P ⊂ U ____ ____ (6) A ⊂ T ____ 𝐴̅ ____ (5) M ⊆ A (7) H ~ P ____ (8) Amanda ∉ M (4) U = (9) Kelly ∈ G ____ ____ Sets can be operated on! We have five operations to discuss. The complement of a set: ̅ A “not A” A The union of sets: The intersection of sets: A ∪B A ∩ B “in A or B or both” “in both A and B” A B A – B “A minus B” B B A x B The Cartesian Product—which is different! ̅ together: Lets do S x D A A B With these we do set operations using Venn diagrams. So let’s get at it! This table was online, and it is incomplete and has extra material, but I thought you would like it anyway . . . Table of set theory symbols Symbol {} A∩B A∪B A⊆B A⊂B A⊄B A⊇B A⊃B A⊅B 2A Symbol Name a collection of elements A={3,7,9,14}, B={9,14,28} objects that belong to set A intersection A ∩ B = {9,14} and set B objects that belong to set A union A ∪ B = {3,7,9,14,28} or set B subset has fewer elements or subset {9,14,28} ⊆ {9,14,28} equal to the set proper subset / strict subset has fewer elements {9,14} ⊂ {9,14,28} subset than the set left set not a subset of right not subset {9,66} ⊄ {9,14,28} set set A has more elements or superset {9,14,28} ⊇ {9,14,28} equal to the set B proper superset / set A has more elements than {9,14,28} ⊃ {9,14} strict superset set B set A is not a superset of set not superset {9,14,28} ⊅ {9,66} B power set all subsets of A power set A=B equality A\B A-B A∆B Example set Ƥ (A) Ac Meaning / definition all subsets of A both sets have the same members all the objects that do not complement belong to set A objects that belong to A and relative complement not to B objects that belong to A and relative complement not to B objects that belong to A or B symmetric difference but not to their intersection A={3,9,14}, B={3,9,14}, A=B A={3,9,14}, B={1,2,3}, AB={9,14} A={3,9,14}, B={1,2,3}, AB={9,14} A={3,9,14}, B={1,2,3}, A ∆ B={1,2,9,14} symmetric difference objects that belong to A or B A={3,9,14}, B={1,2,3}, A ⊖ but not to their intersection B={1,2,9,14} a∈A element of set membership A={3,9,14}, 3 ∈ A x∉A (a,b) not element of no set membership A={3,9,14}, 1 ∉ A ordered pair collection of 2 elements A⊖B A×B Cartesian product |A| cardinality #A cardinality א Ø U aleph empty set universal set natural numbers / whole numbers set (with zero) natural numbers / whole numbers set (without zero) ℕ0 ℕ1 set of all ordered pairs from A and B the number of elements of set A={3,9,14}, |A|=3 A the number of elements of set A={3,9,14}, #A=3 A infinite cardinality Ø={} C = {Ø} set of all possible values ℕ0 = {0,1,2,3,4,...} 0 ∈ ℕ0 ℕ1 = {1,2,3,4,5,...} 6 ∈ ℕ1 ℤ = {...-3,-2,-1,0,1,2,3,...} -6 ∈ ℤ ℤ integer numbers set ℚ rational numbers set ℚ = {x | x=a/b, a,b∈ℕ} ℝ real numbers set ℂ complex numbers set ℂ = {z | z=a+bi, ∞<a<∞, -∞<b<∞} ℝ = {x | -∞ < x <∞} 2/6 ∈ ℚ 6.343434 ∈ ℝ 6+2i ∈ ℂ From http://www.rapidtables.com/math/symbols/Set_Symbols.htm accessed 10/01/12