Deductive Reasoning Homework

Using the statements:
If it is Friday, then I will get paid.
It is Friday.
Write the conclusion.

• It is not Friday
• It is Friday
• I will not get paid
• I will get paid

Using the Law of Syllogism, which of the following completes the statement to form a valid conclusion?
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...

• Look out for the snowplows while driving to school.
• The big test will not be given today.
• The roads will be hard to drive on.
• You should call the school to see if school is canceled.

Which is a valid conclusion from these statements?
If a quadrilateral is a rhombus, then it is a parallelogram.
If a quadrilateral is a parallelogram, then its opposite angles are congruent.

• Opposite angles of a quadrilateral are congruent
• Opposite angles of a rhombus are congruent
• Every quadrilateral is a rhombus
• Every parallelogram is a rhombus

Tags

CCSS.HSG.CO.C.11

Which statement is a valid conclusion based on the argument?
If a polygon is a regular pentagon, then the polygon has exactly five congruent angles.
The polygon is a regular pentagon.

• Therefore, the polygon is a rectangle.
• Therefore, the polygon is a regular quadrilateral.
• Therefore, the polygon has exactly five congruent angles.
• Therefore, the polygon has congruent sides.

(1) If a figure is a square, then it is a polygon.
(2) Figure A is a polygon.
(3)  ???????
What belongs in line 3?

• Figure A is a polygon.
• Figure A is a circle.
• Figure A is a square.
• invalid; nothing belongs in line 3

Tags

CCSS.HSG.CO.A.1

p→q
q→r
∴p→r
Which law is modeled?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

Draw a conclusion from the statement.
Given: If you live in Orlando, then you live in Florida.
Roger lives in Orlando.
Conclusion: ?

• Roger lives in Disney Land
• Roger is an old person.
• Roger lives in Florida
• Roger lives in Orlando

Which is a valid conclusion from these statements?
If the stereo is on, then the volume is loud.
If the volume of the stereo is loud, then the neighbors will complain.

• If the neighbors complain, then the stereo will be loud.
• If the stereo is on, then the neighbors will complain.
• If the stereo is volume is loud, then the stereo is on.
• If the stereo is on, then the volume is loud.

Which of the following statements is valid based on the given scenario?
If Jason plays basketball, then Steve sits on the bench.  
If Steve sits on the bench, then Ronald starts at center.  

• If Steve sits on the bench then Jason plays basketball.
• If Ronald starts at center then Jason plays basketball.
• If Steve sits the bench then Ronald does not start at center.
• If Jason plays basketball then Ronald starts at center.

Tags

CCSS.HSS.CP.A.1

p→q
p
∴q
Which law is modeled?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon