1. MDFP Introduction to Mathematics SETS and Venn Diagrams 2

3. Example 1 120 students commenced a particular university course. Of these 38 had studied Media in Year 12 and 49 had studied Drama in Year 12. If 30 had studied both of these subjects in Year 12 how many had studied neither?

4. M D 120 30 38 – 30 = 8 49 – 30 = 19 63 Draw Venn diagram 120 students commenced a particular university course 38 had studied Media (38) 49 had studied Drama (49) 30 had studied both of these subjects

5. Three sets A, B and C and the universal set, U are such that Find Example 2

6. SOLUTION 150 AB C 6 92 14 11 23 8 77

7. 150 AB C 6 92 14 11 23 8 77 Find Tick every thing in A Tick everything in B. (if not already ticked) Tick everything in C.(if not already ticked) ALL ticked elements represent n(A B C), so................ = 77

8. Example 3 A survey of 100 students revealed that 82 were in Math and 65 were in Critical Thinking. How many students are taking both Math and Critical Thinking? All 100 students are either in Math or Critical Thinking. U

9. Solution 82 + 65 = 147 147 – 100 = 47 82 – 47 = 35 65 – 47 = 18 U 47 MathCT 3518

10. Example 4 At a Cinema, people were surveyed about the movies they watched. 15 people answered Twilight, Shrek and The Avengers. 19 people mentioned Shrek and Twilight. 42 people mentioned Twilight. 21 people mentioned The Avengers and Twilight. 3 people mentioned The Avengers and Shrek but not Twilight. 10 people didn’t mentioned any of the Twilight, Shrek or The Avengers movies. 16 people mentioned The Avengers but not Shrek. 7 people answered only Shrek.

11. Draw a Venn diagram. Use your Venn Diagram to answer the following questions. a) How many people watched The Avengers ? b) How many people watched Shrek? c) How many people watched The Avengers and Shrek? d) How many people watched Twilight but not Shrek or The Avengers? e) How many people were questioned?

12. Solution 1. How many circles do we need? 3: Twilight, Shrek, The Avengers 2. Use the information given to set up the Venn Diagram.

13. Twilight Shrek The Avengers 7 10 15 Venn Diagram: 10 people didn’t mentioned any of the Twilight, Shrek or The Avengers movies. 7 people answered only Shrek. 15 people answered Twilight, Shrek and The Avengers.

14. TwilightShrek The Avengers 10 15 Venn Diagram: continued 17 7 4 63 19 people mentioned Shrek and Twilight. 42 people mentioned Twilight. 21 people mentioned The Avengers and Twilight. 16 people mentioned The Avengers but not Shrek. 3 people mentioned The Avengers and Shrek but not Twilight.

15. TwilightShrek The Avengers 10 15 Now solve the problem: 17 7 4 63 a) How many people watched The Avengers? b) How many people watched Shrek? c) How many people watched The Avengers and Shrek? d) How many people watched Twilight but not Shrek or The Avengers? e) How many people were questioned? 10 + 6 + 15 + 3 = 34 4 + 7 + 15 + 3 = 29 15 + 3 = 18 17 Total = 72 72

16. Complete All Question Sets & Venn Diagrams 2 Any work not completed during class must be completed for homework!