Download Ex 4: State the converse of the conditional statement.

Name
Period ____
GP
LOGIC
I can define, identify and illustrate the following terms
Conditional
Inductive Reasoning
Contrapositive
Statement
Deductive Reasoning
Biconditional
Hypothesis
Inverse
Truth Value
Conclusion
Converse
Negation
Counterexample
Logically
Equivalent
Conjecture
Dates, assignments, and quizzes subject to change without advance notice.
Monday
10
Inductive Reasoning
and
Conditional Statements
Tuesday
11
Block Day
12/13
Converse, Inverse,
Contrapositve
Quiz
Biconditional
Statements
Friday
14
Deductive Reasoning
18
17
Review
TEST 2
Monday, 9/10
(2-1 and 2-2) Inductive Reasoning and Conditional Statements
I can use inductive reasoning to identify patterns and make conjectures
I can determine the hypothesis and conclusion of a conditional statement.
I can write a conditional statement from a sentence.
ASSIGNMENT: pg. 77 (11-13, 16, 20-23, 28,31) pg. 84-87 (13-18)
Tuesday, 9/11
(2-1 and 2-2) Inductive Reasoning and Conditional Statements
I can determine the truth value of a conditional statement.
I can give prove a conditional statement false by giving a counterexample.
I can write the inverse, converse, and contrapositive of a conditional statement.
ASSIGNMENT: pg. 77 (8, 10, 25, 37, 38) pg. 84-87 (10-12, 22, 38, 42-44, 50-52)
Wednesday, 9/12 and Thursday, 9/13
 Quiz: Inductive Reasoning and Conditional Statements
(2-4) Biconditional Statements
Determine the logical equivalence of a set of conditional statements.
I can write a biconditional statement.
I can write a biconditional statement as 2 conditional statements.
I can convert to and from definitions and biconditional statements.
I can determine the truth value of a biconditional statement.
ASSIGNMENT: pg. 99(10, 13, 16-19, 20-23, 38, 41, 52-53)
Friday, 9/14
(2-3) Deductive Reasoning and Verify Conjectures
I can apply the Law of Syllogism and the Law of Detachment in logical reasoning.
ASSIGNMENT: pg. 91 (1, 4-12, 15-18, 23)
Monday, 9/17
Review
I can review for the test in class.
ASSIGNMENT: Pg. 130 (1-9, 11-12,19, 21-25, 28-30)
Tuesday, 9/18
Test 2 – Logic
I can demonstrate knowledge skills, and reasoning ability of ALL previously learned material.
ASSIGNMENT: Test #2
Grade:
TERM:
Conditional Statement
Hypothesis
Conclusion
NOTES: Conditional Statements
DEFINITION:
A statement written in “if-then” format
The phrase following but NOT INCLUDING the word if.
The phrase following but NOT INCLUDING the word then.
Ex 1: Underline the hypothesis and circle the conclusion of the conditional statement below.
If you have an 85% or higher, then you do not need to retest.
Ex 2: Rewrite the statement below as a conditional statement, underline the hypothesis and
circle the conclusion of the conditional statement below.
A car with poor brakes is a menace on the highway.
Conditional:
Ex 3: Rewrite the statement below as a conditional statement, underline the hypothesis and
circle the conclusion of the conditional statement below.
Geometry teachers give their students homework on days that end in ‘y’.
Conditional:
TERM:
Negation
Inverse
DEFINITION:
The denial of a statement (add not)
Formed by negating both the hypothesis and conclusion of a
conditional statement
(add not)
Ex 6: Write the inverse of the conditional statement below.
If you pass the TAKS test, then you will graduate.
Inverse:
Ex 7: Write the inverse of the following statement.
If school is in session, then it is a weekday.
Inverse:
TERM:
Converse
DEFINITION:
Formed by switching the hypothesis and conclusion of a
conditional
Ex 4: State the converse of the conditional statement.
If it is Saturday, then you do not have school.
Converse:
Ex 5: Write the converse of the conditional statement below.
If an angle has a measure of 120, then it is an obtuse angle.
Converse:
TERM:
Contrapositive
DEFINITION:
Formed by negating the hypothesis and conclusion of the
converse.
(switch and add not)
Ex 8: Write both the converse and the contrapositive of
the conditional statement below.
If you run a red light, then you are breaking a traffic law.
Contrapositive:
Ex 9:
Write the contrapositive of the conditional statement below.
If you leave the classroom, then you must take a pass with you.
Contrapositive:
TERM:
Counterexample
DEFINITION:
An example that follows the hypothesis, but not the conclusion.
Ex 10: Give a counterexample for the statement.
If you leave the classroom, then you must take a pass with you.
Counterexample:
Biconditional Statements
Example:
Conditional: If a solution has a pH less than 7, then it is an acid.
Converse: If a solution is an acid, than its pH is less than 7.
Biconditional: A solution is an acid if and only if it has a pH less than 7.
Your Turn:
1) Conditional: If a point is a midpoint, then it divides a segment into two congruent
segments.
Converse: ____________________________________________________________
_______________________________________________________________
_______________________________________________________________
Biconditional: ________________________________________________________
if and only if_____________________________________________________
II. Good definitions are also true when read forwards and backwards. Therefore, we also write
____________________ as biconditional statements.
Example:
Defintion: A triangle is a three-sided polygon.
Biconditional: A figure is a triangle if and only if it is a three-sided polygon.
Your Turn:
1) Definition: A straight angle is an angle whose measure is 180°.
Biconditional: ___________________________________________________
__________________________________________________________
__________________________________________________________
3) Definition: An angle is obtuse when it measures between 90° and 180°.
Biconditional: ___________________________________________________
__________________________________________________________
__________________________________________________________
III. Now, write the conditional statement and the converse from the following biconditional statement.
Biconditional: Two angles are congruent if and only if their measures are equal.
Conditional:________________________________________________________
_____________________________________________________________
Converse: __________________________________________________________
______________________________________________________________
Multiple Choice:
1. Which of the following biconditionals is equivalent to the definition:
“An endpoint is a point at the end of a segment or at the start of a ray.”
a. A point is an endpoint if and only if it is the start of a ray.
b. A point is an endpoint if and only if it lies on a segment or a ray.
c. A point is an endpoint if an only if it is a point.
d. A point is an endpoint if and only if it is at the end of a segment or the start of a ray.
3. Which of the following could be a conditional statement for the following
biconditional?
“You can get your license if and only if you passed the drivers test.”
a. If you take the drivers test, then you will get your license.
b. If you passed the drivers test, then you can get your license.
c. If you can get your license, then you passed the drivers test.
d. All of the above could be conditional statements.
Truth Values
For a biconditional to be true, both the _________________ and the _______________ must be true. If
it is false, then you give a counterexample.
Ex. A rectangle has side lengths of 12 cm and 25 cm if and only if its area is 300 cm2.
Conditional __________________________________________________________
____________________________________________________________________.
Converse: ____________________________________________________________
____________________________________________________________________.
Conditional truth value:______
Converse truth value: ________
Ex. A natural number n is odd  n2 is odd.
Conditional __________________________________________________________
____________________________________________________________________.
Converse: ____________________________________________________________
____________________________________________________________________.
Conditional truth value:______
Converse truth value: ________
Law of Syllogism/Detachment
Use the Law of Syllogism (Transitive property) and the Law of Detachment to determine the
logical conclusion for each of the following. If the statements do not follow either pattern, write
“no valid conclusion”.
Law of Syllogism
(transitive property)
pq
qr
rs
Therefore, p  s
Law of Detachment
p q
p is true
therefore, q is true
1. If 2x + 3 = 17, then x = 7
2x + 3 = 17
Conclusion: ______________________________________________________
2. If Joan goes out with David, then she will watch a movie Saturday night.
Joan watched a movie Saturday night.
Conclusion : _______________________________________________________
3. If I go on vacation, I’ll spend money.
If I spend money, I’ll be broke.
If I’m broke, I’ll have to get another job.
Conclusion: ______________________________________________________
4. If Paul divorces Veronica, then he will not receive his inheritance.
Paul divorces Veronica.
Conclusion: ______________________________________________________
5. If I pass geometry, I won’t have to go to summer school.
If I don’t go to summer school, I’ll get a job.
If I get a job, I’ll make money.
Conclusion: _______________________________________________________
6. If ABCD is a rectangle, then the diagonals are congruent.
The diagonals are congruent.
Conclusion: _______________________________________________________
7. If it’s sunny Saturday, then I’ll go to the beach.
If I go to the beach, then I’ll lay in the sun.
If I lay in the sun, I’ll get a sunburn.
Conclusion: ________________________________________________________
8. If you use Shining Smile toothpaste, then you will be popular.
You are popular.
Conclusion : _______________________________________________________
9. If Chris is a sophomore, he takes English II.
Chris is a sophomore.
Conclusion: ________________________________________________________
10. If the treasure is discovered, then pirate Jack will walk the plank.
The treasure is discovered.
Conclusion: _________________________________________________________
11. If I don’t wear a sweater, I’ll get cold.
If I get cold, I’ll get sick.
If I get sick, I’ll miss the dance.
Conclusion: _________________________________________________________
12. If  1 and  2 are vertical angles, then they are equal.
 1 and  2 are equal.
Conclusion: _________________________________________________________
13. If 2 angles are linear, then they are supplementary.
If 2 angles are supplementary, then their sum is 180º.
Conclusion: __________________________________________________________
14. If Linda takes the bus, she’ll be on time for work.
Linda takes the bus.
Conclusion: __________________________________________________________
15. If Hemlock Bones decodes the secret message, then the agent will live.
The agent lives.
Conclusion: ___________________________________________________________
16. If Mr. Jones gets home on time, then he and Mrs. Jones will attend a meeting.
If Mr. and Mrs. Jones attend a meeting, then Lisa will visit grandma.
If Lisa visits grandman, then she will practice the piano.
If Lisa practices the piano, then she will go to bed late.
Conclusion: ___________________________________________________________
17. If Anakin goes to the dark side, then he will become Darth Vadar.
If he becomes Darth Vadar, then he will wear a black mask.
Conclusion: ____________________________________________________________
18. If Karen goes to Starbucks, then she will buy a Decaf. Mocha.
Karen buys a Decaf. Mocha.
Conclusion: ___________________________________________________________
19. If Ethan is passing all of his classes, then he gets to go to the movies.
Ethan is passing all of his classes.
Conclusion: __________________________________________________________