Logic Cw3 (honors) Deductive Reasoning

a. Make conclusions from the following statements.

• • Kings Fork won the football game.

• • Everyone will go home.

• • This is not valid conclusion

• • Kings Fork Lost the football game

• • Everyone is not celebrate.

Tags

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.11-12.2

CCSS.RI.9-10.1

b. Note which law you used to make a​ conclusion, the Law of Detachment, Law of Syllogism or Law of Contrapositive.

• Law of Detachment, The second statement should have been the conclusion.

• Law of Syllogism, The second statement was the repeated part of the conditional.

• Law of Contrapositive, The conclusion was not negated

a. Make conclusions from the following statements.

• • If we cooperate, then we can go to a movie

• • We'll get the job done faster.

• • If we get the job done faster, we get to leave early.

• None of the conclusions are valid because neither conclusion of the conditional statements is the hypothesis of the other statement.

• • If we don't cooperate, then we can't go to the movies.

Tags

CCSS.RL.11-12.9

CCSS.RL.6.3

CCSS.RL.7.3

CCSS.RL.8.3

CCSS.RL.9-10.3

b. Note which law you used to make a​ conclusion, the Law of Detachment, Law of Syllogism or Law of Contrapositive.

• Law of Detachment

• Law of Syllogism

• Law of Contrapositive

Read the statement below:

Conditional Statement: If the dance is on a Saturday, then the weather will be nice.

The dance is Saturday.

What conclusion can be made? Mark invalid, if needed.

• The weather will be nice
• The dance is not on Saturday
• The weather will not be nice
• Cannot determine the weather

Read the two statements below. Determine if a conclusion can be made. If not, then select invalid.

Statement 1: If I study for more than two hours, then I will do well on my test.

Statement 2: If I study for more than two hours, then I will make at least a 85.

• If I study for more than two hours, then I will do well on my test and make at least a 85.
• If I study for more than two hours, then I will either do well on my test or make at least a 85.
• If I study for more than two hours, then I will do well on my test but not necessarily make at least a 85.
• Invalid

Tags

CCSS.RL.11-12.9

CCSS.RL.6.3

CCSS.RL.7.3

CCSS.RL.8.3

CCSS.RL.9-10.3

Which law is modeled?

• p→q
  ~q

  ∴~p
  

• Law of Contrapositive
• p→q
  p
  ∴q

• Law of Syllogism
• p→r
  r→q

  ∴p→q

• Law of Detachment

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

Tags

CCSS.HSG.CO.A.1

Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

Statement 1: If I study for one hour each day, then I will score well on the exam

Statement 2: I will study from 6pm to 7pm tonite.

• I study for several hours each day.

• I will do well on the exam

• If I do well on the exam, I studied for hours.

• not possible

Tags

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.8.1

CCSS.RI.8.8

Read the two statements below, then make a conclusion, if possible.

Statement 1: If you exercise regularly, then you have a healthy body
Statement 2: If you have a healthy body, then you have more energy

• You have more energy
• If you exercise regularly, then you have more energy
• Invalid

• If you do not have a healthy body, then you do not exercise regularly

Tags

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.11-12.2

CCSS.RI.9-10.1