1. Logic
Lesson 2-2: Logic

2. 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
...B   dog
Example:
Lesson 2-2: Logic

3. 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

4. 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
Lesson 2-2: Logic

5. Law of Detachment - Example
Given: If aliens land, then the world will fall apart.
Aliens land.
Conclusion: The world will fall apart.
Example 2:
Given: If I build a snowman, then he will come to life and sing.
Today I built a snowman.
Conclusion: He will come to life and sing.
Lesson 2-2: Logic

6. 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

7. Law of Syllogism - Example
Given:
If you make a scary face, then the baby will cry.
If the baby cries, then she will not go
to sleep.
Conclusion:
If you make a scary face, then she will not go to sleep.
Lesson 2-2: Logic