Haruka has noticed that it always seems to smell nice just before it rains. One day she smells the “rain smell” and thinks it will rain soon.
Haruka is using ____to form a ____.
Select one:
a.
deductive reasoning, conclusion
b.
inductive reasoning, conjecture
c.
inductive reasoning, paradox
d.
deductive reasoning, premise
b. inductive reasoning, conjecture
Read the following statement.
All adults were once children and all children like to play, so Grandpa must have liked to play at one time.
Select the premise(s) and conclusion that best fit the scenario.
Select one:
a.
Premise(s): grandpa used to like to play
Conclusion: grandpa used to be a child
b.
Premise(s):
• all adults were children
• all children like to play
• grandpa used to be a child
Conclusion: grandpa used to like to play
c.
Premise(s): all children like to play
Conclusion: grandpa used to like to play
d.
Premise(s):
• grandpa used to like to play
• all adults were children
• grandpa used to be a child
Conclusion: all children like to play
b. Premise(s):
• all adults were children
• all children like to play
• grandpa used to be a child
Conclusion: grandpa used to like to play
Read the following statement:
All fish have gills and, therefore, cannot breathe air.
The best counterexample to the statement is
Select one:
a.
A crab has gills and therefore cannot breathe air.
b.
A lungfish has simple lungs and can be in air or water.
c.
A crocodile has lungs and lives in water and on land.
d.
A perch has no lungs and therefore must live in the water.
b. A lungfish has simple lungs and can be in air or water.
Read the following statement:
Eric plays hockey and is in the NHL, therefore everyone in the NHL plays hockey.
The statement is best described as
Select one:
a.
correct reasoning
b.
flawed reasoning
c.
paradoxical reasoning
d.
circular reasoning
b. flawed reasoning
The statement that uses circular reasoning is
Select one:
a.
A square has 4 sides of equal length and 4 angles that measure 90°.
b.
Lisa is wearing plaid pajama pants so Lisa likes plaid.
c.
The sum of the angles in a triangle is 180° because each angle in an equilateral triangle is 60°.
d.
All right triangles also contain two acute angles.
c. The sum of the angles in a triangle is 180° because each angle in an equilateral triangle is 60°.
Fred, Ginger, Roger, and Esther are siblings. One is a farmer, one is a dog trainer, one is a rodeo clown, and one is a teacher.
• Esther and Roger eat supper with the rodeo clown.
• Ginger and Fred play cards with the dog trainer.
• Roger plays basketball with the dog trainer and the farmer.
The dog trainer is
Select one:
a.
Ginger
b.
Fred
c.
Roger
d.
Esther
b. Fred
Read the following conjecture and proof.
Conjecture: The sum of three consecutive whole numbers is divisible by 3.
Proof:
• Let Equation 020, Equation 018, and Equation 019represent the consecutive whole numbers.
• The sum of the three numbers is Equation 020.
• 3 is a factor, so the sum is divisible by 3.
The proof is
Select one:
a.
valid.
b.
invalid: It didn’t reach the desired conclusion.
c.
invalid: It has used circular reasoning.
d.
invalid: It cannot be determined whether is divisible by 3.
a. valid.
Prove that when two odd numbers are added together, their sum is always even.
Let 2n + 1 represent the first odd number.
Let Answer
m + Answer
represent the other odd number.
2n + 1 + Answer
m + Answer
* add the two odd number together
= Answer
n + Answer
m + Answer
* combine like terms
=Answer
(n + m + Answer
) * factor out the GCF
Notice that the expression above represent Answer
which means the expression is Answer
.
Therefore, when two odd numbers are added together the sum is Answer
.
The proof is invalid.
The proof is incomplete and does not adequately support the conjecture or reach the desired conclusion. It is unclear how the expression "Answer" is related to the sum of the two odd numbers or how it can be identified as even. Additionally, no justification or reasoning is provided for the claim made in the final statement.
Elizabeth claims that she has proven that 2 = 3 with the following proof.
Scan Elizabeth's proof and indicate whether her step is:
Right - all math rules were followed correctly
Wrong - an algebra mistake occurred or a fundamental math no-no occurred
OK - the work in that step is good but it was based on a previous incorrect step
Premise: a space plus space b space equals space c Right or Wrong or OK?
Step 1 left parenthesis 3 a space minus space 2 a right parenthesis space plus space left parenthesis 3 b space minus space 2 b right parenthesis space equals space left parenthesis 3 c space minus space 2 c right parenthesis blank
Step 2 space space space space space space 3 a space up diagonal strike negative space 2 a end strike space plus space 3 b space up diagonal strike negative space 2 b end strike space equals space 3 c space minus space 2 c blank
Step 3 space space space space space space space space space space space space space space space space space space space space space space space space space 3 a space plus space 3 b space equals space up diagonal strike 3 c end strike space plus 2 a space plus space 2 b space minus space 2 c blank
Step 4 space space space space space space space space space space space space space space space 3 a space plus space 3 b space minus space 3 c space equals space 2 a space plus space 2 b space minus space 2 c blank
Step 5 space space space space space space space space space space space space space space space space space 3 left parenthesis a space plus space b space minus space c right parenthesis space equals space 2 left parenthesis a space plus space b space minus space c right parenthesis blank
Step 6 space space space space space space space space space space space space space space space space fraction numerator 3 up diagonal strike left parenthesis a space plus space b space minus space c right parenthesis end strike over denominator up diagonal strike left parenthesis a space plus space b space minus space c right parenthesis end strike end fraction space equals space fraction numerator 2 up diagonal strike left parenthesis a space plus space b space minus space c right parenthesis end strike over denominator up diagonal strike left parenthesis a space plus space b space minus space c right parenthesis end strike end fraction blank
Step 7 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 3 space equals space 2 blank
Right, Wrong, OK
Step 1: OK
Step 2: OK
Step 3: OK
Step 4: OK
Step 5: OK
Step 6: Wrong
Step 7: OK
A 3×3 grid can be filled in with the letters A, B, and C, so each row and column contains each letter once.
For example:
C B A
B A C
A C B
Use the following clues to complete the grid. Rows go left and right, while columns go up and down.
• In the first row, A is the first letter.
• In the second row, C is somewhere to the right of A.
• In the second column, B is the last letter.
blank blank blank
blank blank blank
blank blank blank
A B C
Using the given clues, we can fill in the grid as follows:
A B C
C A B
B C A