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WorksheetsInductive and Deductive Reasoning
Total questions: 63
Worksheet time: 2hrs 55mins
Inductive Reasoning means...
Guessing
Testing and observing patterns to make conjectures
Explaining why
Adding numbers together
Reasoning based on facts, definitions, accepted properties, and the laws of logic is called ____________ reasoning.
Inductive
Deductive
The product of any two odd numbers is _____________
A, D, G, J, _____
12, 15, ___, 21, ____, 27
12, 17, 22, 27, ___, ___
A, D, G, J, _____
23, 33, ___, 53, ___, 73
If something is an angle, then it is acute. What is an appropriate counter-example?
70⁰
45⁰
120⁰
True. There is no counterexample.
Which of the following provide a counterexample to the claim:
"If two angles are supplementary, then they are not congruent."
40° and 140°
80° and 80°
30° and 150°
90° and 90°
All numbers that are divisible by 2 are divisible by 4
Which is a counterexample to the following statement?
If an angle is obtuse, then it is 125° .
90°
57°
160°
180°
What does deductive reasoning use to form its arguments?
patterns
specific cases
observed examples
facts, definitions, accepted properties, and laws of logic
Determine if inductive or deductive reasoning is being used.
Blake knows that if there is a snow storm, then the roads will be slick.
The roads are slick.
Therefore, Blake concludes there was a snow storm.
Inductive
Deductive
Write the following statement as a conditional statement:
A dog with proper training will not misbehave.
If a dog has proper training, then it will not misbehave.
If a dog does not behave, then it had proper training.
A dog had proper training if and only if it will not misbehave.
What is a conjecture?
A statement believed to be true based on observations.
An example which disproves an hypothesis.
A statement that reverses the hypotheses and the conclusion.
This is used to prove that a conjecture is false.
Counterexample
Inductive Reasoning
Concluding statement
Negation
Deductive reasoning means...
Guessing without any information
Sounding knowledgeable even when you are not
Testing and observing patterns to make conjectures
Drawing conclusions from situations based on facts and definitions
Every time you do all your homework your grades improve. You conclude that doing homework improves your grades.
deductive
inductive
Using definitions, theorems, and postulates to make a conclusion
inductive
deductive
AND 28 is even
THEN 28 is divisible by 2
AND 24...27...30...?
THEN the next term is going to be 33
If Tom goes fishing then he brings a pole.
If Tom brings his pole then he catches a fish.
The product of any two odd numbers is _____________
All numbers that are divisible by 2 are divisible by 4
Inductive or Deductive?
A scientist dips a platinum wire into a solution containing salt, passes the wire over a flame, and observes that it produces an orange-yellow flame. She does this with many other solutions that contain salt, finding that they all produce an orange-yellow flame. She states "A solution that contains salt produces a orange-yellow flame in a flame test".
Inductive Reasoning
Deductive Reasoning
Inductive or Deductive?
Amanda was learning to drive when her father told her to never run the car if the overheat light comeson. Last summer while driving to Anchorage, her over heat light turned on so she turned off the car and called for help.
Inductive Reasoning
Deductive Reasonng
Inductive or Deductive?
Your teacher tells the class that no credit will be given to assignments that show no work. For two months you do your homework. Last week, your assignment had a couple of problems where no work was shown. You received no credit for the assignment.
Inductive Reasoning
Deductive Reasoning
Inductive or Deductive?
Hunter notices that every day his math teacher wears what seems to be a different tie everyday. He starts keeping track of what his teacher wears. After one semester, Hunter approaches his teacher and states, "I think you wear a different tie every day, do you have a
180 different ties?"
Inductive Reasoning
Deductive Resasoning
If it is snowing heavily, then school will be canceled.
If school is canceled, the big test will not be given today.
It is snowing heavily, then...
If the stereo is on, then the volume is loud.
If the volume of the stereo is loud, then the neighbors will complain.
Use Law of Syllogism to draw a conclusion.
If the sun is shining it is a beautiful day. If it is a beautiful day then we will go go hiking.
If the sun is not shining, we will not go hiking.
If the sun is shining then we will go hiking.
No conclusion can be made.
If we go hiking, then it is a beautiful day.
Use Law of Syllogism to draw a conclusion.
If a number is divisible by 10, then it is divisible by 2. If a number is divisible by 2, then it is even.
If a number is divisible by 10, then it is even,
If a number is even, then it is divisible by 10.
If a number is divisible by 2, then it is even.
If a number is even, then it is divisible by 2.
Using the Law of Detachment, draw a conclusion based on the statements given:
If a plane flies to China, then it will be a long flight. Sarah bought a ticket to China.
Sarah will get stuck in the security line.
Sarah will have a long flight.
Sarah will need to bring a neck pillow and headphones.
Sarah will get stuck with a middle seat on the plane.
Using the Law of Syllogism, write a new conditional statement that follows from the pair of true statements.
If you study, then you will pass the test. If you pass the test, then you will pass the class.
If you study, then you will pass the class.
If you pass the test, then you should study.
If you pass the class, then you will pass the test.
If you study, then you will pass the test.
If I go to the movie, then I’ll eat popcorn.
If I eat popcorn, then I’ll enjoy the movie.
No valid conclusion possible
Yes, using the Law of Detachment
Yes, using the Law of Syllogism
If I miss my bus, then I’ll be late for school.
I miss my bus.
No valid conclusion possible
Yes, using the Law of Detachment
Yes, using the Law of Syllogism
If this wind keeps up, then we will lose some trees.
We lose some trees.
No valid conclusion possible
Yes, using the Law of Detachment
Yes, using the Law of Syllogism
If a person is a librarian, then they read books.
If a person is a friend of Dana’s, then they read books.
No valid conclusion possible
Yes, using the Law of Detachment
Yes, using the Law of Syllogism
The product of any two odd numbers is _____________
Mei draws three pairs of parallel lines that are each intersected by a third line. In each figure, she measures a pair of alternate interior angles.
What is a reasonable conjecture for Mei to make by recognizing a pattern and using inductive reasoning?
When a pair of parallel lines are intersected by a third line, the alternate interior angles are congruent.
When a pair of parallel lines are intersected by a third line, all of the angles formed are congruent.
When a pair of parallel lines are intersected by a third line, the alternate interior angles are acute.
When a pair of parallel lines are intersected by a third line, all of the angles formed are obtuse.
Jamar draws three pairs of parallel lines that are each intersected by a third line. In each figure, he measures a pair of same-side interior angles.
What is a reasonable conjecture for Jamar to make by recognizing a pattern and using inductive reasoning?
When a pair of parallel lines are intersected by a third line, the same-side interior angles are acute.
When a pair of parallel lines are intersected by a third line, all of the angles formed are supplementary.
When a pair of parallel lines are intersected by a third line, the same-side interior angles are supplementary.
When a pair of parallel lines are intersected by a third line, all of the angles formed are acute.
Kathryn draws three pairs of intersecting lines. In each figure, she measures a pair of vertical angles.
What is a reasonable conjecture for Kathryn to make by recognizing a pattern and using inductive reasoning?
When a pair of lines intersect, all of the angles formed are congruent.
When a pair of lines intersect, the vertical angles are congruent.
When a pair of lines intersect, the vertical angles are acute.
When a pair of lines intersect, all of the angles formed are right angles.
Jasmine draws three scalene triangles. In each figure, she measures each of the angles.
What is a reasonable conjecture for Jasmine to make by recognizing a pattern and using inductive reasoning?
In a scalene triangle, none of the angles are congruent.
In a scalene triangle, all of the angles are acute.
In a scalene triangle, none of the angles are right angles.
In a scalene triangle, one of the angles is obtuse.
Which statement is true about this argument?
Premises: If an angle measure is greater than 90°, then the angle is an obtuse angle. The measure of ∠C∠C is 102°.
Conclusion: ∠C∠C is an obtuse angle.
The argument is valid by the law of syllogism.
The argument is not valid because the premises are not true.
The argument is valid by the law of detachment.
The argument is not valid because the conclusion does not follow from the premises.
Which statement is true about this argument?
Premises: If a triangle is an isosceles triangle, then it has two sides of equal length. If a triangle has two sides of equal length, then it has two angles of equal measure.
Conclusion: If a triangle is an isosceles triangle, then it has two angles of equal measure.
The argument is valid by the law of detachment.
The argument is valid by the law of syllogism.
The argument is not valid because the premises are not true.
The argument is not valid because the conclusion does not follow from the premises.
Which statement is true about this argument?
Premises: If a parallelogram has a right angle, then it is a rectangle. Parallelogram PQRSParallelogram PQRS has a right angle.
Conclusion: Parallelogram PQRSParallelogram PQRS is a rectangle.
The argument is valid by the law of syllogism.
The argument is not valid because the conclusion does not follow from the premises.
The argument is valid by the law of detachment.
The argument is not valid because the premises are not true.
