Lesson 2-2
Logic
Lesson 2-2: Logic
1
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:
.B
DOGS
.A
A =poodle ... a dog
B= horse ... NOT a dog
...B   dog
Lesson 2-2: Logic
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For all..., every..., if...then...
Example1: All right angles are congruent.
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.
Lesson 2-2: Logic
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To Show Relationships using Venn Diagrams:
A
B
AB
Blue or Brown (includes Purple) … AB
Lesson 2-2: Logic
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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...
Lesson 2-2: Logic
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Solution:

Twenty-four members of Mu Alpha Theta
went to a Mathematics conference.
Three members were on cross
country and football teams…
The above sentence tells you two draw
overlapping circles and put 3 in CCF
One-third
CC
5
Football
3
1
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….
Lesson 2-2: Logic
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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.
Band
15
CC
5
Football
3
1
Mu Alpha Theta
Lesson 2-2: Logic
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Law of Detachment
Given:
a true conditional statement and
the hypothesis occurs
pq is true
p is given
Conclusion:
the conclusion will also occur
q is true
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Law of Detachment - Example
Example 1:
Given: If three points are collinear, then the points are all on one line.
E, F, and G are collinear.
Conclusion: E, F, and G are all on one line.
Example 2:
If I find $20 in the street, then I’ll take you to the movies.
On October 10 I found $20 in the street.
Conclusion: I will take you to the movies.
Given:
Lesson 2-2: Logic
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Law of Syllogism
Given:
Two true conditional statements and
the conclusion of the first is the hypothesis of the second.
pq and qr
Conclusion:
If the hypothesis of the first occurs, then the conclusion of the
second will also occur.
pr
Lesson 2-2: Logic
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Law of Syllogism - Example
Example:
Given:
If it rains today, then we will not have a picnic.
If we do not have a picnic, then we will not see our
friends.
Conclusion:
If it rains today, then we will not see our friends.
Lesson 2-2: Logic
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