$100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements...
-
Upload
sabrina-chandler -
Category
Documents
-
view
244 -
download
0
Transcript of $100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements...
$100 $100 $100 $100 $100
$200
$300
$400
$500
$200 $200 $200 $200
$300 $300 $300 $300
$400 $400 $400 $400
$500 $500$500 $500
Inductive Reasoning and Logic
Conditional Statements
Angle and Segment Addition
Deductive Reasoning
Postulates and Proof
Answer
Inductive Reasoning: Reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction
Back
Inductive Reasoning and Logic for $300
Fill in the blanks:The _______ of a statement
is whether a statement is true or false. A statement is false if one __________ can be found.
Answer
The Truth Value of a statement is whether a statement is true or false. A statement is false if one Counterexample can be found.
Back
Inductive Reasoning and Logic for $500
Draw a truth table for the following compound statement:
(Pv~Q)^R
Answer
Back
P Q ~Q (Pv~Q) R (Pv~Q)^R
T T F T T T
T T F T F F
T F T T T T
T F T T F F
F T F F T F
F T F F F F
F F T T T T
F F T T F F
Conditional Statements for $100
Identify the hypothesis and conclusion in the following conditional statement:
If we are playing Jeapordy then, the students try to talk too much after questions
Answer
Hypothesis: We are playing Jeapordy
Conclusion: The students try to talk to much after questions
Back
Conditional Statements for $200
Write the following statement as a conditional in if-then form:
Studying Descartes makes students happy
Conditional Statements for $300
Determine whether or not the following statement is reversible (i.e. whether or not the converse is true). If it is, write the statement as a biconditional:
Two lines that are skew are not coplanar.
Answer
No, they could be parallel.
Example of biconditional:
A triangle is a polygon with 3 sides
It is a triangle if and only if it is a polygon with three sides
Back
Conditional Statements for $500
Write the conditional, converse, inverse, and contrapositive of the following statement and determine the truth value for each:
All squares are rectangles
Answer
Back
Conditional: If it is a square then it is a rectangle. True
Converse: If it is a rectangle then it is a square. False
Inverse: If it is not a square then it is not a rectangle. False
Contrapositive: If it is not a rectangle then it is not a square. True
Answer
Deductive Reasoning- Uses facts, rules, definitions, or properties to reach logical conclusions
Back
Answer
If p implies q and q implies r are true, then p implies r is also true.
[(p→q)^(q→r)]→(p→r)
Back
Deductive Reasoning for $400
Use the law of detachment to draw a conclusion from the two statements given:
1)I can go to the concert if I can afford to buy a ticket
2)I can go to the concert
Answer
No conclusion possible:
Conditional: If I can afford to buy a ticket, then I can go to the concert
Thus, (p→q)^q => Not the Law of Detachment: [(p→q)^p]→q
Back
Deductive Reasoning for $500
Use the Law of Syllogism to draw a conclusion from the two statements given:
1) If a number is a multiple of 64, then it is a multiple of 8
2) If a number is a multiple of 8, then it is a multiple of 2
Answer
If a number is a multiple of 64, then it is a multiple of 2 by the Law of Syllogism
[(p→q)^(q→r)]→(p→r)
Back
Answer
Back
Paragraph (informal) Proof – A paragraph that explains why a conjecture for a given situation is true.
Postulates and Proof for $200
Write a Paragraph Proof showing that given that M is the midpoint of PQ, then PM MQ
Answer
From the definition of midpoint of a segment, PM = MQ. This means that PM and MQ have the same measure. By the definition of congruence, if two segments have the same measure, then they are congruent. Thus PM MQ
Back
Postulates and Proof for $300
Write a two column proof showing that:
If AB = BC;AB =-5x+3;BC = -4+2x
Then, x = 1
Answer
Back
Statements ReasonsAB = BC; AB = -5x + 3
BC = -4 + 2xGiven
-5x + 3 = -4 + 2x Substitution+5x – 5x + 3 = -4 + 2x + 5x Addition Prop. of Equality3 = -4 + 7x Simplify3 + 4 = -4 + 4 + 7x Addition Prop. of Equality7 = 7x Simplify7/7 = (7x)/7 Division Prop. of Equality1 = x Simplifyx = 1 Symmetric Prop. of Algebra
Answer
Back
Statements Reasons
(5x-2)/2 = 9 Given
2* (5x-2)/2 = 9 *2 Multiplication Prop of Equality
5x-2 = 18 Simplify
5x-2+2 = 18 + 2 Addition Prop. of Equality
5x = 20 Simplify
(5x)/5 = 20/5 Division Prop of Equality
x = 4 Simplify
Answer1) Through any two points, there is exactly one line2) Through any three non-collinear points there is
exactly one plane3) A line contains at least two points4) A plane contains at least 3 points5) If two points lie in a plane, then the entire line
containing those points lies in that plane6) If two lines intersect, then their intersection is
exactly one point7) If two planes intersect then their intersection is
line
Back
Angle and Segment Addition for $100
Name the Property of congruence of angles that justifies the statement:
If Angle 1 Angle 2,
then Angle 2 Angle 1
Angle and Segment Addition for $200
Name the Postulate that justifies the statement:
Given: Points A,B,C are collinear and point B lies between A and C, then
AB + BC = AC
Angle and Segment Addition for $300
Given that <PQR and <RQS form a linear pair, solve for x
R
7x-323x+22
PQ S
Angle and Segment Addition for $400
Write a two column proof showing that if AC = 40 and points A, B,C are collinear, then x = 4
AnswerStatements Reasons
AC = 40;A,B,C are Collinear
AB = 2x; BC = 6x+8
Given
AB + BC = AC Segment Addition Postulate
2x + 6x + 8 = 40 Substitution
8x + 8 = 40 Combining Like Terms/Simplify
8x + 8 – 8 = 40-8 Subtraction Prop. of Equality
8x = 32 Simplify
(8x)/8 = 32/8 Division Prop. of Equality
X = 4 Simplify Back