CSCI 246 - Lesson 1 Quiz Question Draw an arrow diagram for the - - PowerPoint PPT Presentation

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CSCI 246 - Lesson 1 Quiz Question Draw an arrow diagram for the - - PowerPoint PPT Presentation

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CSCI 246 - Lesson 1 Quiz Question Draw an arrow diagram for the following relation: A = {1,2,3} B = {a,b,c} R = {(1,a), (a,b), (2, c), (3, a)} Lesson 1 Review Logical Statements Universal Existential Conditional Sets Roster Notation

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CSCI 246 - Lesson 1

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Quiz Question

Draw an arrow diagram for the following relation: A = {1,2,3} B = {a,b,c} R = {(1,a), (a,b), (2, c), (3, a)}

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Lesson 1 Review

Logical Statements Universal Existential Conditional Sets Roster Notation Builder Notation Cartesian Product

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Lesson 1 Review

Logical Statements “For every student in the class, that student has studied calculus”

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Lesson 1 Review

Logical Statements “For every student in the class, that student has studied calculus” Universal

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Lesson 1 Review

Logical Statements “There exists a gpa for every student”

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Lesson 1 Review

Logical Statements “There exists a gpa for every student” Existential - Universal

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Lesson 1 Review

Sets Roster Notation Builder Notation

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Lesson 1 Review

Sets S = {Hufflepuff, Gryffindor, Ravenclaw, Slytherin}

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Lesson 1 Review

Sets S = {Hufflepuff, Gryffindor, Ravenclaw, Slytherin} Roster

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Lesson 1 Review

Sets S = {Hufflepuff, Gryffindor, Ravenclaw, Slytherin} How would you write this in set builder notation?

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Lesson 1 Review

Sets S = {Hufflepuff, Gryffindor, Ravenclaw, Slytherin} How would you write this in set builder notation?

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Lesson 1 Review

Cartesian Product A = {a, b} B = {star, moon} AxB = ?

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Lesson 1 Review

Cartesian Product A = {a, b} B = {star, moon} AxB = {(a, star), (a, moon), (b, star), (b, moon)}

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Lesson 1 Review

Cartesian Product A = {a, b} B = {star, moon} AxB = {(a, star), (a, moon), (b, star), (b, moon)} What’s the Cardinality?

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Lesson 1 Review

Cartesian Product A = {a, b} B = {star, moon} AxB = {(a, star), (a, moon), (b, star), (b, moon)} What’s the Cardinality? 4

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Lesson 2 Review

Relations Subsets Arrow Diagrams Functions

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Lesson 2 Review

Relations Subsets Defn: Let A, B be sets, a Relation R is a subset

  • f the cartesian product of AxB
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Lesson 2 Review

Relations Subsets Defn: Let A, B be sets, a Relation R is a subset

  • f the cartesian product of AxB

Set of all numbers

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Lesson 2 Review

Relations Subsets Defn: Let A, B be sets, a Relation R is a subset

  • f the cartesian product of AxB

Set of all numbers R= {(x,y) exists in R^2 | x < y }

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Lesson 2 Review

Relations Path Diagrams A = {1,2,3} B = {a,b,c} R = {(1,a), (a,b), (2, c), (3, a)}

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Lesson 2 Review

Functions Defn: A function f from A (domain) to B (Range) is a relation on A x B s.t.

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Lesson 2 Review

Functions Defn: A function f from A (domain) to B (Range) is a relation on A x B s.t.

  • 1. (A) every x in A there exists (E) in B s.t. (x,y)

exists in f

  • 2. If (x,y) in f and (x,z) in function f, then y = z
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Homework 1 (group)

  • 1. What kind of statement is: “for every cat there

exists a vaccine” ?

  • 2. What kind of set notation is:
  • 3. Write the above set in the opposite notation.
  • 4. Give the cartesian product for: A = {1,2}, B={z,

x}, C = {red, blue}

  • 5. What is the cardinality of the cartesian product

above?

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Homework 1 (group)

  • 6. Give arrow diagram for: XxY (cartesian

product) where: X = {1,2,3}, Y = {enterprise, voyager}

  • 7. Is the above a function?
  • 8. Why or why not?
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Homework 1 (Individual)

  • 1. What type of statement is:
  • 2. Is the set {1,3,5} equal to {1, 5, 3}? Why?
  • 3. Give the elements in the set {x | x is the square
  • f an integer and x<100}
  • 4. Change this set to set builder notation:
  • a. {0, 3, 6, 9, 12}
  • 5. Make an arrow diagram for {(1,3), (0, 0), (2,

6), (4, 12), (3, 9)}.

  • 6. Is this a function? Can you find the relation?