Conditionals and Deductive Reasoning

Identify:

 $If\ p\rightarrow q\ is\ true,\ and\ p\ occurs\ then\ q\ occurs.$  

• Law of Syllogism

• Law of Contrapositives

• Law of Detachment

• Law of Diminishing Returns

Identify:

 $If\ p\rightarrow q\ is\ true,\ and\ q\rightarrow r\ is\ true,\ then\ p\rightarrow r\ is\ true.$  

• Law of Syllogism

• Law of Contrapositives

• Law of Detachment

• Law of Diminishing Returns

If possible use the Law of Detachment to make a conclusion.

If the band plays, then the people are happy.

The people are happy.

• The band plays

• The band didn't play

• The people are not happy

• Cannot determine

Tags

CCSS.HSS.CP.B.6

If possible use the Law of Syllogism to make a conclusion.

If Jon wins the contest, then he will get a lot of money.

If Jon gets a lot of money, then he will pay off his mortgage.

• If Jon wins the contest, he will pay off his mortgage.

• If Jon loses the contest, he will not pay off his mortgage.

• If Jon pays off his mortgage, he will win the contest.

• Cannot determine

If possible use the Law of Syllogism to make a conclusion.

If my teacher assigns homework, then I can't play video games.

If my teacher assigns homework, then I do it after school.

• If my teacher assigns homework, then I play video games.

• If I do my homework after school, then I can play video games.

• If my teacher doesn't assign homework, then I can play video games.

• Cannot determine

If possible use the Law of Detachment to make a conclusion.

If the doctor suspects a broken bone, then he will take an x-ray.

Lilly's arm is red and swollen, after falling off her bike.

• The doctor will not take an x-ray.

• The doctor will take an x-ray.

• Lilly will not go to the doctor.

• Cannot determine

Tags

CCSS.HSS.CP.A.3

If possible use the Law of Detachment and the Law of Syllogism to make a conclusion.

If a river is the longest in the region, then it is the longest on the continent.

If a river in the region is more than 1412 miles long, then it is the longest in the region.

The Calumet River is 1624 miles long.

• The Amazon is the longest on the continent.

• The Calumet River is not the longest in the region

• The Calumet River is less than 1412 miles long.

• The Calumet River is the longest on the continent.

If possible use the Law of Syllogism to make a conclusion.

If Dad works late, then we'll order take-out food.

If we order take-out food, then we'll get pizza.

• If Dad works late, then we'll get pizza.

• If Dad orders take-out, it will be pizza.

• We will order Chinese.

• Cannot determine

If possible use the Law of Detachment to make a conclusion.

If a student gets 5 tardies, then they will receive a detention.

Billy has a detention.

• Billy has 6 tardies.

• Billy is not in detention.

• Billy has 5 tardies.

• Cannot determine

If possible use the Law of Detachment and the Law of Syllogism to make a conclusion.

If person lives in Chicago, then they live in Illinois.

If a person lives in Illinois, then they live in the Midwest.

Michael lives in Chicago.

• Michael does not live in Illinois.

• Michael lives in the Midwest.

• Michael doesn't live in the Midwest.

• Steve lives on the East Coast.