2.4 Deductive Reasoning and Logic Laws

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

Tags

CCSS.RI.8.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.8.8

CCSS.RL.7.1

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.

Tags

CCSS.RI.8.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.8.8

CCSS.RI.7.1

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.

Tags

CCSS.HSG.CO.C.11

(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.2.G.A.1

If an angle is 40⁰, then it is acute.
∠A is 40⁰.
Using the Law of Detachment, what is the logical statement to conclude?

• ∠A is complementary to ∠B
• ∠A is acute.
• ∠A is obtuse.
• ∠A is 40⁰

Use Law of Syllogism to make 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.

What can be concluded from the following statements?
If Tom goes fishing then he brings a pole.
If Tom brings his pole then he catches a fish.

• If Tom goes fishing then he catches a fish.
• If Tom brings his pole then he goes fishing
•  If Tom catches a fish then he brought his pole.
• If Tom brings his pole then he catches a fish.

Tags

CCSS.RI.8.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.8.8

CCSS.RI.7.1

Determine if the conjecture is valid by the Law of Syllogism.
Given: If you are in California, then you are in the west coast. If you are Los Angeles, then you are in California.
Conjecture: If you are in Los Angeles, then you are in the west coast.

• No, the conjecture is not valid.
• Yes, the conjecture is valid.

Obtuse angles are greater than 90 degrees.  This angle is 110 degrees, so it is obtuse. 

• Deductive
• Inductive

Tags

CCSS.4.G.A.1