Name: ___________________________ Block: ____
Ch 2: Reasoning and Proof
PRACTICE PROBLEMS
Notes
Assignment
Score
Learning Target(s)
2.2 Conditional
Statements
22
2.3 Deductive
Reasoning
21
Venn Diagrams
Ch 2 Review
What am I confident about?
Where do I need to spend more time?
Am I weak on a prerequisite skill?
What am I going to do if I am weak?
9
21
Learning Targets:
Use inductive reasoning; write definitions as conditional statements
Use deductive reasoning to form a logical argument
Use symbolic notation to represent logical arguments
Use Venn diagrams to represent relationships
Unit 1 Syllabus: Ch 2 Reasoning and Proof
Block Date
Topic
1
T 9/2
Algebra Skills Review
W 9/3
2
Th 9/4
Geometry Diagnostic
F 9/5
3
M 9/8
2.1 Use Inductive Reasoning
T 9/9
2.2 Analyze Conditional
Statements
4
W 9/10
2.3 Apply Deductive
Th 9/11 Reasoning
5
F 9/12
Venn Diagrams
M 9/15
6
T 9/16
Review Day
W 9/17
7
Th 9/18 Ch 2 Quest
F 9/19
Homework
Worksheet: Algebra Review
Worksheet: Review
Practice Problems: 2.1/2.2
Conditional Statements
Practice Problems: 2.3
Deductive Reasoning
Practice Problems: Venn
Diagrams
Practice Problems: Review
Ch 2
Spiral Review
***Syllabus subject to change due to weather, pep rallies, illness, etc
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HW: 2.2 Conditional Statements
Rewrite the conditional statement in if-then form. Underline the hypothesis and circle
the conclusion.
1. It is time for dinner if it is 6 p.m.
2. There are 12 eggs if the carton is full.
3. A number is divisible by 6 if it is divisible by 2 and 3.
4. An obtuse angle is an angle that measures more than 90 and less than 180.
5. Geometry is offered only during even numbered blocks.
Decide whether the statement is true or false. If false, provide a counterexample.
6. The equation 4x  3  12  2x has exactly one solution.
2
7. If x  36 , then x must be equal to 18 or –18.
8. Thanksgiving is celebrated on a Thursday.
9. If you visited Springfield, then you’ve been to Illinois.
Using symbols, write the converse, inverse and contrapositive of each statement.
Converse
Inverse
Contrapositive
10. ~p  ~q
11. ~ hk
22
Write the converse, inverse and contrapositive of each statement.
If you like hockey, then you go to the hockey game.
12. Converse:
13. Inverse:
14. Contrapositive:
If x is odd, then 3x is odd.
15. Converse:
16. Inverse:
17. Contrapositive:
10. If mP = 90, then P is a right angle.
18. Converse:
19. Inverse:
20. Contrapositive:
Write the converse of each of the following conditional statements, and then write the biconditional
with symbolic form in parenthesis. ( )
21. If an angle is acute, then its measure is less than 90o
Converse:_________________________________________________________(________________)
Biconditional: ________________________________________________________(________________)
22. If the measure of an angle is 180 o, then it is a straight angle.
Converse:__________________________ ____________________________________(________________)
Biconditional: _________________________________________________________(________________)
HW: 2.3 Deductive Reasoning
21
Use the Law of Detachment to make a valid conclusion in the situation.
1. If you get a hit, then your baseball team will win. You hit a home run.
2. If Rylee gets promoted, then Callie will also be promoted. Rylee is promoted
Use the Law of Syllogism to write the statement that follows from the pair of statements that are given.
3. If Moose is hungry when he goes to the pizza shop, then he’ll finish a whole pizza.
If Moose eats a whole pizza, then he goes through a pitcher of soda.
4.If a triangle has two angles of 60°, then the triangle is equiangular. If a triangle is equiangular, then it
is also equilateral.
Determine if a conclusion can be made from each set of statements. If possible, write the conclusion AND
the law that was used. If not possible, write INVALID.
5.
If A and B are right angles, then the angles are congruent.
The angles are congruent.
6.
If two lines are perpendicular, then their slopes are opposite reciprocals. If the slopes of two lines
are opposite reciprocals, then the product of their slopes is -1.
7.
If a number is divisible by 6, then it is divisible by 2.
The number is 36.
8.
If two lines have equal slopes, then the lines are parallel.
If the lines are parallel, then the lines do not intersect.
9.
If today is Saturday, then there is no school
There was no school today.
Determine if a conclusion can be made from the given statements. If a conclusion can be made, state the
conclusion then state which law was used, the Law of Detachment, Law of Syllogism, or with a
combination of contrapositive. If a conclusion cannot be made, state INVALID. (2 point each)
10.
p→q
p
11.
a→b
c → ~b
12.
q→r
~r
13.
r→s
s→t
14.
q→r
r
15.
p → ~q
~r → q
s → ~r
Symbolic Notation
Let p represent “Math is fun”, and let q represent “Math is difficult”.
Translate the following into symbolic form.
16. Math is not fun. ______________________________
17. Math is fun or math is difficult. ______________________________
18. Math is not fun and math is difficult. ______________________________
Translate the following from symbolic form to written form.
19.
q p
20.  q
21. p  q
HW: Venn Diagrams
1.
9
2.
3. The Venn diagram below represents all mammals, place an ‘X’ in the space that represents
dolphins that are mammals and can swim. Shade the region that represents mammals that can
swim but are not dolphins.
Mammals
can swim
dolphins
cannot
swim
Carefully read the following Venn diagrams and select the best answer.
4.
5.
6. During lunch at Stone Bridge High School, seventy-one students chose juice and sixty-two students
chose milk. Thirty-two students chose both juice and milk. Each student chose at least one of these
beverages. How many students ate lunch at the Stone Bridge High School cafeteria?
7. The Webster PAL took a survey asking students in which three sports they would like to participate in
a summer program: baseball, soccer or football. They received the following results:







24 students like baseball only
8 students like football only
6 students like baseball and soccer
4 students like baseball and football
4 students like soccer and football
2 students like all three sports
66 students participated in the survey
How many students chose only soccer? Explain how you arrived at your answer
Use the given information to draw a Venn diagram.
8.
Some fish are yellow.
Some fish are blue.
Some fish are yellow and blue.
All fish live in water.
9.
Some football players run track.
Some cheerleaders run track.
No football players are cheerleaders.
HW: Chapter 2 Quest Review: Reasoning and Proof
Identify the hypothesis and the conclusion of each sentence. Underline the hypothesis once
and the conclusion twice.
1. If the weather is warm, then we should go swimming.
2. If the groundhog sees its shadow, then there will be six more weeks of winter.
Rewrite the sentence in if-then form.
3. Today is Monday if yesterday was Sunday.
4. Logic puzzles are a lot of fun.
5. An object measures 12 inches if it is one foot long.
6. A number is divisible by 4 if it is divisible by 8.
Determine whether the statement is true or false. If false, provides a counterexample.
7. February 14 is Valentine’s Day.
8. If you visited the White House, then you’ve been to Maryland.
2
9. If x  16 , then x must equal 8 or 8.
10. If it is Monday, then it is Memorial Day.
11. If you like tennis, then you play on the tennis team.
For each statement write the converse, inverse and contrapositive.
12. If x is even, then 2x  1 is odd.
Converse:
Inverse:
Contrapositive:
21
13. If mP = 115, then P is obtuse.
Converse:
Inverse:
Contrapositive:
14.
~mn
Contrapositive:
Converse:
Inverse:
Determine if a conclusion can be made from the argument. If so, identify the argument as Law of
Detachment or Law of Syllogism AND write the conclusion. If none, write invalid.
15. If it is Friday night, then we will eat pizza. We eat pizza.
_____________________________________________________________
________
16. If it is July 4th, then we will have a picnic. If we have a picnic, then we will have fireworks.
________________________________________
________
_____________________________________________________________
17. If a parallelogram is a square, then it is a rhombus. ABCD is a square.
________ _____________________________________________________________
18. If Jay thinks positive, then he will feel good about math. If Jay feels good about math, then he will
have more success at it.
____________
________
_____________________________________________________________
19. If it is summer, then I go swimming. It is summer.
_____________
________ _____________________________________________________________
Venn Diagrams
20. Describe each region.
A = fruit loops
B = fruity pebbles
A
IV
21.
B
I
II
III
In a breakfast survey of 100 students,
52 ate pancakes
62 ate cereal
46 ate fruit
29 ate pancakes and cereal
27 ate cereal and fruit
25 ate pancakes and fruit
15 ate all three
How many did not eat the given
breakfasts?