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## SET THEORY

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**SET THEORY**Chapter 2**Set – collection**• School of fish • Gaggle of geese • Pride of lions • Pod of whales • Herd of elephants**Set – usually named with a capital letter.**• Well defined A is the set of the first three lower case letters of the English alphabet.**Elements of the set**A is the set of the first three lower case letters of the English alphabet. a, b, and c are elements of set A**Natural Numbers (Counting Numbers)**N = {1, 2, 3, . . . }**Three ways of defining a set:**• List A = {1,2,3} • Description A is the set of the first three counting numbers. • Set Builder Notation**Universe**• Empty set**Example**The set of natural numbers greater than 12 and less than 17.**Example**{x | x = 2n and n = 1, 2, 3, 4, 5}**Example**{3, 6, 9, 12, . . . }**Example**The set of the first 10 odd natural numbers.**Subsets**A is a subset of B if every element of A is also an element of B.**List all the subsets of {a,b,c}**• { } • {a} • {b} • {c} • {a,b} • {a,c} • {b,c} • {a,b,c}**List all the subsets of {a,b,c}**• Proper Subsets: { } , {a} , {b} , {c} , {a,b} , {a,c} , {b,c} • THE Improper Subset: {a,b,c}**Subset Notation**Let A = {a,b,c} {a} A “The set of a is a subset of A.” (think: The set of a is a proper subset OR IS EQUAL TO A.) {a} A “The set of a is a proper subset of A.”**True or False? A = {b,c,f,g}**{b,f} A {b,f} A**True or False? A = {b,c,f,g}**{b,f} A True {b,f} A True**True or False? A = {b,c,f,g}**{b,d} A**True or False? A = {b,c,f,g}**{b,d} A False Because d A**True or False? A = {b,c,f,g}**{b,c,f,g} A**True or False? A = {b,c,f,g}**{b,c,f,g} A True {b,c,f,g} A**True or False? A = {b,c,f,g}**{b,c,f,g} A True {b,c,f,g} A False Because {b,c,f,g} = A**U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u},**C = {r,u,w,y}**U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u},**C = {r,u,w,y}**U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u},**C = {r,u,w,y}**U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u},**C = {r,u,w,y}**U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u},**C = {r,u,w,y}**U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u},**C = {r,u,w,y}**U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u},**C = {r,u,w,y}**U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u},**C = {r,u,w,y}**U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u},**C = {r,u,w,y}**U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u},**C = {r,u,w,y}**U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u},**C = {r,u,w,y}**U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u},**C = {r,u,w,y}**Three types of numbers.**• Nominal • Ordinal • Cardinal “The student with ticket 50768-973 has just won second prize – four tickets to the big game this Saturday.”