1 / 23

LOGIC

LOGIC. Chapter 2 – Lesson 2. LOGIC. Determine truth values of negations, conjunctions, and disjunctions, and represent them using Venn diagrams. Objectives. Find counterexamples. LOGIC. Keywords- Statement – a sentence that is either true or false

tan
Télécharger la présentation

LOGIC

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. LOGIC Chapter 2 – Lesson 2

  2. LOGIC • Determine truth values of negations, conjunctions, and disjunctions, and represent them using Venn diagrams. • Objectives • Find counterexamples.

  3. LOGIC • Keywords- • Statement – a sentence that is either true or false • Truth value – either (T) for true or (F) for false for a statement • Negation – giving the opposite meaning to a statement • Compound statement – two or more statements joined by AND or OR • Conjunction – a compound statement using only AND • Disjunction – a compound statement using only OR • Truth table – a convenient way for organizing the truth values of a statement

  4. LOGIC • For example: • p: A rectangle is a quadrilateral • What is it’s truth value? • TRUE • ~p: A rectangle is NOT a quadrilateral • What is it’s truth value? • FALSE

  5. LOGIC • p: A rectangle is a quadrilateral • q: A rectangle is convex • p and q: A rectangle is a quadrilateral, AND a rectangle is convex • What is it’s truth value? • TRUE • Since both p and q are true, the conjunction p and q, also written as , is true • The word OR uses the symbol:

  6. LOGIC

  7. LOGIC • A. Use the following statements to write a compound statement for the conjunction p and q. Then find its truth value. • p: One foot is 14 inches.q: September has 30 days.r: A plane is defined by three non-collinear points. Answer: p and q:One foot is 14 inches, and September has 30 days. Although q is true, p is false. So, the conjunction of p and q is false.

  8. LOGIC B.Use the following statements to write a compound statement for ~q  ~r. Then find its truth value.p: June is the sixth month of the year.q: A square has five sides.r: A turtle is a bird. A. A square has five sides and a turtle is not a bird; true. B. A square does not have five sides and a turtle is not a bird; true. C. A square does not have five sides and a turtle is a bird; false. D. A turtle is not a bird and June is the sixth month of the year; true.

  9. LOGIC B.Use the following statements to write a compound statement for ~q  ~r. Then find its truth value.p: 6 is an even number.q: A cow has 12 legs.r: A triangle has 3 sides. A. A cow does not have 12 legs or a triangle does not have 3 sides; true. B. A cow has 12 legs or a triangle has 3 sides; true. C. 6 is an even number or a triangle has 3 sides; true. D. A cow does not have 12 legs and a triangle does not have 3 sides; false.

  10. LOGIC

  11. LOGIC A. Construct a truth table for ~p q. Step 1 Make columns with the heading p, q, ~p, and ~p q. Answer:

  12. LOGIC A. Construct a truth table for ~p q. Step 2 List the possible combinations of truth values for p and q. Answer:

  13. LOGIC A. Construct a truth table for ~p q. Step 3 Use the truth values of p to determine the truth values of ~p. Answer:

  14. LOGIC A. Construct a truth table for ~p q. Step 4 Use the truth values of ~p and q to write the truth values for ~p q. Answer:

  15. LOGIC B.Construct a truth table for p (~q  r). Step 1 Make columns with the headings p, q, r, ~q, ~qr, and p  (~q  r).

  16. LOGIC B.Construct a truth table for p (~q  r). Step 2 List the possible combinations of truth values for p, q, and r.

  17. LOGIC B.Construct a truth table for p (~q  r). Step 3 Use the truth values of q to determine the truth values of ~q.

  18. LOGIC B.Construct a truth table for p (~q  r). Step 4 Use the truth values for q and r to write the truth values for ~q r.

  19. LOGIC B.Construct a truth table for p (~q  r). Step 5 Use the truth values for ~q rand p to write the truth values for p (~q r). Answer:

  20. LOGIC B. Which sequence of Tsand Fs would correctlycomplete the last columnof the following truth tablefor the given compound statement? (p  q)  (q  r) A. T B. T C. T D. TT T F TT T T TF T F FT T T TF T F TT T F TF F F F

  21. LOGIC DANCING The Venn diagram shows the number of students enrolled in Monique’s Dance School for tap, jazz, and ballet classes. A. How many students are enrolled in all three classes? The students that are enrolled in all three classes are represented by the intersection of all three sets. Answer: There are 9 students enrolled in all three classes.

  22. LOGIC DANCING The Venn diagram shows the number of students enrolled in Monique’s Dance School for tap, jazz, and ballet classes. B. How many students are enrolled in tap or ballet? The students that are enrolled in tap or ballet are represented by the union of these two sets. Answer: There are 28 + 13 + 9 + 17 + 25 + 29 or 121 students enrolled in tap or ballet.

  23. LOGIC DANCING The Venn diagram shows the number of students enrolled in Monique’s Dance School for tap, jazz, and ballet classes. C. How many students are enrolled in jazz and ballet, but not tap? The students that are enrolled in jazz and ballet and not tap are represented by the intersection of jazz and ballet minus any students enrolled in tap. Answer: There are 25 + 9 – 9 or 25 students enrolled in jazz and ballet and not tap.

More Related