UNIT 10 Logic and Venn Diagrams Data Sheets

Transcription

1 NIT 10 Logic and Venn Diagrams Data Sheets Data Sheets Logic Puzzle Logic Puzzle Logic Puzzle 10.4 Two Way Tables Two Way Tables Constructing Two Way Tables 10.7 Illustrating Sets 10.8 Identifying Sets 10.9 Identifying and Illustrating Sets Intersection and nion Sets and Venn Diagrams Definitions sing Set Notation Describing Sets Describing Sets Logic Problems and Venn Diagrams Logic Table Logic Table

2 Data Sheet Logic Puzzle Rachel, Tia and Millie are sisters. You need to deduce which sister is 9 years old, which one is 12 and which one is 14. You have two clues: Clue 1 : Clue 2 : Tia's age is not in the 4-times table. Millie's age can be divided exactly by the number of days in a week. se the logic table to solve this problem.

3 Data Sheet Logic Puzzle my, Emma and Hannah are sisters. Their ages are 2 years, 7 years and 10 years. Clue 1 Clue 2 Emma is older than Hannah. Emma's age is a prime number. se the logic grid below to solve the problem

4 Data Sheet Logic Puzzle In akers Row there are 4 houses, each numbered 1, 2, 3 or 4. The following people live in akers Row, one in each house: Tom, lice, Ellis and Gemma se these clues to find out who lives in which house, using the logic table below. Clue 1 Clue 2 Clue 3 Clue 4 The number of Tom's house is an even number. The number of Ellis's house is an odd number. The number of lice's house is greater than the number of Tom's house. The number of Gemma's house is less than the number of Ellis's house.

5 Data Sheet 10.4 Two Way Tables 1 Emma collected information about the cats and dogs that students in her class have. She filled in the table below, but missed out one number. Has a dog Does not have a dog Has a cat Does not have a cat (a) (b) (c) (d) If there are 30 students in Emma's class, what is the missing number? How many students own at least one of these pets? Do more students own cats rather than dogs? Could it be true that some of the students do not have any pets?

6 Data Sheet 10.5 Two Way Tables 2 The table below gives information about the students in a class. Lefthanded Righthanded oys Girls (a) (b) (c) (d) (e) How many right-handed girls are there in the class? How many left-handed boys are there in the class? How many girls are there in the class? How many of the students are left-handed? How many students are in the class?

7 Data Sheet 10.6 Constructing Two Way Tables In en's class there are 12 girls and 18 boys. There are 6 students who travel to school by route taxi and the others walk. en and dam are the only boys who travel by route taxi. (a) (b) How many students are there in the class? How many girls walk to school? oys Girls Route taxi Walk

8 Data Sheet 10.7 Illustrating Sets The sets and consist of numbers taken from the whole numbers 0, 1, 2, 3,.., 9, so that Set = { 4, 7, 9 } Set = { 1, 2, 3, 4, 5 } Illustrate these sets in a Venn diagram.

9 Data Sheet 10.8 Identifying Sets The whole numbers from 1 to 10 are placed in a Venn diagram (a) Write down the members of the sets. = { } = { } (b) Describe the sets and in words.

10 Data Sheet 10.9 Identifying and Illustrating Sets Set contains the whole numbers greater than 6 but less than 12. Set contains the whole numbers greater than 2 but less than 10. (a) List set and set. = { } = { } (b) Illustrate the sets and on the Venn diagram below, including all the whole numbers from 1 to 15.

11 Data Sheet Intersection and nion The sets X and Y are shown in this Venn diagram. X Y Find: (a) the intersection of X and Y : { } (b) the union of X and Y ; { } (c) the complement of X : { }

12 Data Sheet Sets and Venn Diagrams

13 Data Sheet Definitions : universal set : the intersection of and : the union of and ' : the complement of and : is a subset of : empty set

14 Data Sheet sing Set Notation Describe in words, set and set. 2. Find (a) = { } (b) = { } (c) = { } (d) = { } (e) ' = { } (f) ' = { } (g) ( )' = { } (h) ' = { } (i) ' = { }

15 Data Sheet Describing Sets 1 se set notation to describe the shaded regions of these diagrams. (a) (b) C

16 Data Sheet Describing Sets 2 (a) On this diagram, shade the region that represents ( ) C' C (b) On this diagram, shade the region that represents C' C

17 Data Sheet Logic Problems and Venn Diagrams In a class there are 8 students who play football and basketball 7 students who do not play football or basketball 13 students who play basketball 19 students who play football. Illustrate these facts on a Venn diagram, and find how many students there are in the class. F Total number of students in class =

18 Data Sheet Logic Table

19 Data Sheet Logic Table