1. Venn Diagrams

2. Venn diagrams:  Show relationships between different sets of data.  Can represent conditional statements.  Is usually drawn as a circle.  Every point IN the circle belongs to that set.  Every point OUT of the circle does not belong. Example: A = poodle... a dog B = horse... NOT a dog. B DOGS.A.A...B   dog

3. For “ALL”..., “EVERY”..., “IF...THEN”... All right angles are congruent. Example 1: Example 2:Every rose is a flower. If two lines are parallel, then they do not intersect. lines that do not intersect parallel lines Flower Rose Congruent Angles Right Angles Example 3:

4. Example: Everyone who drives 80 mph is breaking the law. Conditional: If you are caught driving 80 mph, then you are breaking the law. breaking the law drives at 80 mph

5. Example: Everyone who drives 80 mph is breaking the law. Fact: John drove 80 mph. Conclusion: breaking the law drives at 80 mph John broke the law.  John Conditional:If John drives 80 mph, then he is breaking the law.

6. Try: All living creatures sleep. Conditional: If you are a living creature, then you sleep. Living creatures Things that sleep

7. Try : All living creatures sleep. Conditional: If an animal is a kitten, then it sleeps. Living creatures Things that sleep Fact: A kitten is a living thing. Conclusion:A kitten sleeps.  kitten If an animal is a kitten, then it is a living creature.

8. For “SOME”… Purple “OR” Orange (all regions) …A  B A B Purple “AND” Orange (overlapping region)… A  B

9. Example: Some women don’t like chocolate. Conditional: If you are a women, then you might not like chocolate. don’t like chocolate Women

10. Example: Some women don’t like chocolate. Conditional: If Mary is a women, then she might not like chocolate. Fact: Mary is a women. Conclusion: Mary might not like chocolate. don’t like chocolate Women

11. Try: Some students take Spanish. Conditional: If you are a student, then you might take Spanish. Students Spanish

12. Try: Some students take Spanish. Conditional: If Mike is a student, then he might take Spanish. Students Spanish Fact: Michael is a student Conclusion: Mike might take Spanish

13. For “NO” Conditional: If a person is a girl, then it is not a boy. No object in one set is another set Boys Girls Example: No girl is also a boy

14. Conditional: If Rachel is a girl, then she is not a boy. Boys Girls Example: No girl is also a boy Fact: Rachel is a girl. Conclusion: Rachel is not a boy.

15. Conditional: If a person is a baby, then it doesn’t drink coffee. No babies drink coffee. babies Drink coffee Try

16. Example: Twenty-four members of Mu Alpha Theta went to a Mathematics conference. One-third of the members ran cross country. One sixth of the members were on the football team. Three members were on cross country and football teams. The rest of the members were in the band. How many were in the band? Draw a Venn Diagram and take one sentence at a time...

17. Solution: 2. Three members were on cross country and football teams… 3 The above sentence tells you two draw overlapping circles and put 3 in CC  F 1. Twenty-four members of Mu Alpha Theta went to a Math conference. 3. One-third of the members ran cross country. 24 / 3 = 8; 8 members run cross country. So put 5 in cross country as there are already 3 in cross country. CCFootball 5 4. One sixth of the members were on the football team. 24/6 = 4; 4 members play football. So put 1 in football as there are already 3 in football. 1 Continued….

18. Solution: Continued……  The rest of the members were in the band. How many were in the band?  Out of 24 members in Mu Alpha Theta, 9 play football or run cross country.  Therefore, 15 are in the band. CC Football 3 5 1 Band 15 Mu Alpha Theta