truth tables and venn diagrams. truth tables truth tables are a very convenient way to organize the...
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Truth Tables and Venn Diagrams
Truth Tables
Truth Tables are a very convenient way to organize the truth values of statements.
Disjunction
p q
Conjunction
p q p q p q
Truth Tables
p q ~p p q
Truth Tables
p q ~p p q
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: A = poodle ... a dog
B = horse ... NOT a dog
.BDOGS
.A
For all..., every..., if...then...
All right angles are congruent.
Congruent Angles
Right Angles
Example1:
Example 2: Every rose is a flower.
Flower
Rose
Example 3: If two lines are parallel, then they do not intersect.
lines that do not intersect
parallel lines
To Show Relationships using Venn Diagrams:
Blue or Red (includes Purple) … AB
A B
A B
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...
Solution:
• Three members were on cross country and football teams…
3The above sentence tells you two draw overlapping circles and put 3 in CCF
Twenty-four members of Mu Alpha Theta went to a Mathematics conference.
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.
CC Football
5
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….
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
35 1
Band
15
Mu Alpha Theta