Truth Tables and Venn Diagrams

1. Truth Tables and Venn Diagrams

2. Truth Tables Truth Tables are a very convenient way to organize the truth values of statements.

3. Truth Tables

4. Truth Tables

5. DOGS A = poodle ... a dog .A B = horse ... NOT a dog . B 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. Example:

6. For all..., every..., if...then... All right angles are congruent. Example1: Congruent Angles Example 2: Every rose is a flower. Right Angles Flower • lines that do • not intersect Rose parallel lines Example 3: If two lines are parallel, then they do not intersect.

7. To Show Relationships using Venn Diagrams: Blue or Red (includes Purple) … AB A B A  B

8. 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? Hint: Draw a Venn Diagram and take one sentence at a time...

9. Solution: Twenty-four members of Mu Alpha Theta went to a Mathematics conference. • Three members were on cross country and football teams… CC Football 3 1 5 The above sentence tells you two draw overlapping circles and put 3 in CCF • 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. • 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. Continued….

10. Example: 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 Band 3 5 1 15 Mu Alpha Theta