1. Truth Tables and Venn Diagrams

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

3. Truth Tables p q ~p

4. Truth Tables p q ~p

5. Venn diagrams: . .A 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.
A = poodle ... a dog
B = horse ... NOT a dog . B
DOGS .A
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:B
A  B
Blue or Red (includes Purple) … 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: 3 Three members were on cross country and football teams…
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