1. Review Sheet Chapter Two
Symbols:
Venn Diagrams:
Overlaps: Some shared portion (both true)
No overlap: nothing in common
Completely inside: all of the smaller are part of the bigger; but not the other way around
Logic Laws:
Law of syllogism: pq, qr, so pr example: If it snows, we miss school. If we miss school, you sleep in. If it snows, you sleep in.
Law of detachment: pq is true statement; so if p is true, then q must be
example: If you have 4 tardies, you get ISS. Tym has 4 tardies. Tym will get ISS
Statements:
Test Taking Tips:
Stop and think – don’t hurry through; Does the sentence make any sense
Symbol Λ V ~   
Logical
And Or
Not
Therefore
If …, then
If and only if
Meaning
Both
Either
Opposite
conclusion
conditional
biconditional C
B and C share and so do C and D
B and D don’t
All A’s are B’s, but not all B’s are A’s B A D
Statement
Symbols
Hint
Example
Conditional
P  Q
Hypothesis, Conclusion
If it snows, we get out of school.
Converse
Q  P
Flip
If we get out of school, it snows.
Inverse
~P  ~Q
Negate
If it didn’t snow, we don’t get out of school.
Contrapositive
~Q  ~P
Both
If we don’t get out of school, then it didn’t snow.

2. Pictures and games, but also internet
Pictures, but no games

3. Contrapositive is a flip and a negate
Triangles and Logic
SSM:
no help
Contrapositive is a flip and a negate
flip changes order of statements and negate adds a not to both
(remember a double negative is a positive!)

4. if and only if is a biconditional statement represented by 
or is represented by 
Therefore is represented by 
and is represented by 
Let m represent:
Angle A is obtuse.
Let n represent:
Angle B is obtuse.
Which is a symbolic representation of the following argument?
Angle A is obtuse if and only if Angle B is obtuse.
Angle A is obtuse or Angle B is obtuse.
Therefore, Angle A is obtuse and Angle B is obtuse.
A. m → n B. m → n C. m ↔ n D. m ↔ n
m ∧ n m ∨ n m ∧ n m ∨ n
∴ m ∨ n ∴ m ∧ n ∴ m ∨ n ∴ m ∧ n
m  n
Angle A is obtuse if and only if Angle B is obtuse.
Angle A is obtuse or Angle B is obtuse.
Therefore, Angle A is obtuse and Angle B is obtuse.
m  n
 m  n

5. if and only if is a biconditional statement represented by 
or is represented by 
Therefore is represented by 
and is represented by 
pq
pq
pq

6. Check to see which answers make sense when you read them
Triangles and Logic
SSM:
Check to see which answers make sense when you read them
D does not fit the pattern
Just because some snakes live in the water does not mean that they are fish

7. Ch 2
Coordinate Relations and Transformations
SSM:
test each area *
Flute and oboe is the intersections of the Flute and Oboe circles. Overlaps with other circles must be eliminated because of the word “only”

8. look for conclusion that has the parts of the statements
Ch 2
Coordinate Relations and Transformations
SSM:
look for conclusion that has the parts of the statements
draw figures to illustrate answers
Rhombus is parallelogram and parallelogram has opposite angles congruent; so combine rhombus has opposite angles congruent

9. Negate the hypotheses and the conclusion.
Ch 2
Coordinate Relations and Transformations
SSM:
inverse  negate
Remember the order:
converse flip
inverse negate
contrapositive both
Negate the hypotheses and the conclusion.

10. Equilateral triangles have 3 sides equal and
Ch 2
Reasoning, Lines, and Transformations
Some are both
All I are E
All E are I
None are both
Equilateral triangles have 3 sides equal and
isosceles triangle have 2 sides equal
SSM:
draw triangles

11. Brent takes a vacation appears in the second line
Ch 2
Reasoning, Lines, and Transformations
SSM:
think of it as a puzzle
~p
p  ~q q
Brent works this summer is in first line normally and in the third line with a not.
Brent takes a vacation appears in the second line
If .., then … .  not ~ therefore

12. eliminate statements that are false
Ch 2
Reasoning, Lines, and Transformations
SSM:
draw a rhombus
eliminate statements that are false
Given mentions parallelograms, opposite angles and rhombus.
Plug rhombus in for parallelogram in if then statement.
(Look for any answer that has two of these terms)

13. remember order: converse Flip inverse Negate contrapositive Both
Ch 2
Reasoning, Lines, and Transformations
SSM:
remember order: converse Flip inverse Negate contrapositive Both
Converse says to flip the conclusion and the hypotenuse order.