Show:
Valid/Invalid True/False
Make a Statement
Conjectures
&
Counterexamples
Prove it!
Laws of Deduction
100
For a biconditional statement to be true, ____________ and ___________ must be true.
the conditional and converse
100
Write a conditional statement from the following: Two angles that are complimentary are acute.
If two angles are complimentary, then they are acute.
100
Describe what a counterexample is.
A counterexample is one example where the statement is false.
100
Describe what paragraph proofs, flow chart proofs, and 2-column proofs are.
Paragraph -- Statements and justifications are written within the body of a paragraph, sentences flow together. Flow Chart -- Bubbles are used to write the statements in, justifications are written below bubbles, and arrows show the next step in the proof. 2-column -- proof with numbered lines within a table, left column is for statements, right column is for justifications.
100
______________ is the type of reasoning where a statement is determined true because specific cases are true.
Inductive Reasoning
200
Determine whether the Law of Detachment was used validly or invalidly...be able to explain. GIVEN: If you fly from Texas to California, then you travel from the central to the Pacific time zone. If you travel from the central to the Pacific time zone, then you gain two hours. CONJECTURE: If you gain two hours, then you have flown from Texas to California.
INVALID. The conjecture should be the converse of what was stated.
200
Identify the hypothesis and conclusion... An angle is obtuse if it's measure is 107 degrees
Hypothesis: If it's measure is 107 degrees Conclusion: An angle is obtuse
200
Determine whether the statement is true or find a counterexample. There are 28 days in February.
counterexample: leap year, there are 29 days in Feb.
200
Determine the justification that was used: 1. Angle ABC is congruent to Angle XYZ 1. GIVEN 2. measure angle ABC = measure angle XYZ 2. _______
Definition of congruency
200
In the law of detachment, you are given a conditional statement and an 'extra sentence'... What does the extra sentence have to 'match' in order for the law to be used correctly?
Extra sentence must match the hypothesis of the given conditional.
300
Determine if the use of deductive reasoning is valid or invalid... Be able to explain. GIVEN: If you want to go on a field trip, you must have a signed permission slip. Megan wants to go on a field trip. CONJECTURE: Megan must have a signed permission slip.
Valid. The extra sentence matches the hypothesis, and the conjecture matches the conclusion.
300
Given the statement "If p, then q" tell how the inverse, converse, and contrapositive would read.
Inverse: "If not p, then not q" Converse: "If q, then p" Contrapositive: "If not q, then not p"
300
Find a counterexample for the following statement: For all non-zero integers, -x < x
When x equals any negative number.
300
Determine the correct statement given the justification: 1. Angle MJL and angle ADF form a linear pair 1. GIVEN 2. _____________________ 2. LINEAR PAIR THM.
Angle MJL and angle ADF are supplementary
300
Using the Law of Detachment, determine the correct conjecture: GIVEN: If you multiply a positive and negative number, then the product will be negative. I multiplied 6 and -2.
Then answer is negative (-12)
400
Determine the truth value of the conditional statement: If a nickel is made of gold, then we are in England.
True! False hypothesis and false conclusion = true.
400
Write or state the biconditional statement that comes from: Sophomores are in 10th grade.
A student is a sophomore if and only if they are in 10th grade.
400
Make a conjecture... The square of a natural number is always _____________
positive
400
Using the Transitive property of congruence, what can be concluded from the following information? The Biology book is congruent to the Geometry book; and the Biology book is also congruent to the Algebra book.
The Geometry and Algebra book are congruent.
400
In the Law of Syllogism, if the given information is two conditional statements set up correctly, (if p, then q. if q, then r) then the conjecture should be ___________.
If p, then r.
500
Determine the truth value of the biconditional and explain. A point is between two other points if and only if all three points are collinear.
TRUE: between means that points must be collinear..and converse and conditional are true.
500
Determine the conditional statement that can be written from: If it rained last night, then the sidewalk is wet. If the sidewalk is wet, then there are puddles in the parking lot.
If it rained last night, then there are puddles in the parking lot.
500
Make a conjecture... If x = 2n-1, where n is an integer, x is always ___________
odd
500
Write the justification for each step on slide 1
1. given 2. def. of midpoint 3. vertical angles theorem 4. transitive prop (steps 2,3) 5. transitive prop (steps 4, 3) 6. def. angle bisector
500
Using the Law of Syllogism, what is your conjecture for the following: GIVEN: If your battery is drained, then your car might not start. If you leave your car lights on overnight, then your car battery will drain.
If you leave your car lights on overnight, then your car might not start.