Docsity
Log inSign up
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources
Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study
Go to the blog

Law of Syllogism, Exercises of Mathematics

Unitech Training Academy - West Monroe CampusMathematics

Follow From Statements by either the Law of Detachment or Law of Syllogism and Use Law of Detachment to Make a Valid Conclusion in the Situation.

Typology: Exercises

2021/2022

Uploaded on 02/11/2022

uzmaan
uzmaan 🇺🇸

3.1

(9)

216 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Extra Practice with 2.1 and 2.3 Name _______________________________
Determine if statement (3) follows from statements (1) and (2) by either the Law of Detachment or Law of
Syllogism. If it does, state which law was used. If it does not, write invalid.
1. (1) If an angle measures more than
90
, then it is not acute. Law of Detachment
(2)
120m ABC
.
(3)
ABC
is not acute.
2. (1) All
45
angles are congruent. Invalid
(2)
AB
(3)
A
and
B
are
45
3. (1) If you order the apple pie, then it will be served with ice cream. Law of Detachment
(2) Matthew ordered the apple pie.
(3) Matthew was served ice cream.
4. (1) If you wear the school colors, then you have school spirit. Law of Syllogism
(2) If you have school spirit, then the team feels great.
(3) If you wear the school colors, then the team will feel great.
5. (1) If you can eat too much turkey, then you will get sick. Invalid
(2) Kinsley got sick.
(3) Kinsley ate too much turkey.
6. (1) If
2
is acute, then
3
is obtuse. Law of Syllogism
(2) If
3
is obtuse, then
4
is acute.
(3) If
2
is acute, then
4
is acute.
In problems 7-10, decide whether inductive or deductive reasoning is used to reach the conclusion. Explain
your reasoning.
7. Angela knows that Walt is taller than Peter. She also knows that Peter is taller than Natalie. Angela
reasons that Walt is taller than Natalie. Deductive, it is logic and order
8. Josh know that Brand X computers cost less than Brand Y computers. All other brands that Josh knows
of cost less than Brand X. Josh reasons that Brand Y cost more than all the other brands. Inductive, based
on observations.
9. For the past three Wednesdays, the cafeteria has served macaroni and cheese for lunch. Dana concludes
that the cafeteria will serve macaroni and cheese for lunch this Wednesday. Inductive, based on
observations.
10. If you live in Nevada and are between the ages of 16 and 18, then you must take driver’s education to get
your license. Anthony lives in Nevada, is 16 years old, and has his driver’s license. Therefore, Anthony took
driver’s education. Deductive, based on logic and order.
pf2

Partial preview of the text

Download Law of Syllogism and more Exercises Mathematics in PDF only on Docsity!

Extra Practice with 2.1 and 2.3 Name _______________________________

Determine if statement (3) follows from statements (1) and (2) by either the Law of Detachment or Law of Syllogism. If it does, state which law was used. If it does not, write invalid.

1. (1) If an angle measures more than 90 , then it is not acute. Law of Detachment

(2) m  ABC  120 .

(3)  ABC is not acute.

2. (1) All 45 angles are congruent. Invalid

(2)  A   B

(3)  A and  B are 45 

  1. (1) If you order the apple pie, then it will be served with ice cream. Law of Detachment (2) Matthew ordered the apple pie. (3) Matthew was served ice cream.
  2. (1) If you wear the school colors, then you have school spirit. Law of Syllogism (2) If you have school spirit, then the team feels great. (3) If you wear the school colors, then the team will feel great.
  3. (1) If you can eat too much turkey, then you will get sick. Invalid (2) Kinsley got sick. (3) Kinsley ate too much turkey.

6. (1) If  2 is acute, then  3 is obtuse. Law of Syllogism

(2) If  3 is obtuse, then  4 is acute.

(3) If  2 is acute, then  4 is acute.

In problems 7-10, decide whether inductive or deductive reasoning is used to reach the conclusion. Explain your reasoning.

  1. Angela knows that Walt is taller than Peter. She also knows that Peter is taller than Natalie. Angela reasons that Walt is taller than Natalie. Deductive, it is logic and order
  2. Josh know that Brand X computers cost less than Brand Y computers. All other brands that Josh knows of cost less than Brand X. Josh reasons that Brand Y cost more than all the other brands. Inductive, based on observations.
  3. For the past three Wednesdays, the cafeteria has served macaroni and cheese for lunch. Dana concludes that the cafeteria will serve macaroni and cheese for lunch this Wednesday. Inductive, based on observations.
  4. If you live in Nevada and are between the ages of 16 and 18, then you must take driver’s education to get your license. Anthony lives in Nevada, is 16 years old, and has his driver’s license. Therefore, Anthony took driver’s education. Deductive, based on logic and order.

Use law of detachment to make a valid conclusion in the situation.

  1. If you get a hit, then your baseball team will win. You hit a home run. Your team wins the baseball game.
  2. If Rylee gets promoted, then Callie will also be promoted. Rylee is promoted. Callie is also promoted.
  3. Any time Kendra runs in a cross country race, if she runs a strong race, then she wins. In the cross country race last Saturday, Kendra ran her best race. Kendra won the race.
  4. If two integers are added together, then the result is an integer. You add an integer x to another integer y. The sum is an integer.
  5. If you double a negative number, then the result is a smaller number. You calculate 2x , where x <0. 2x<x
  6. If an integer is divided by one of its factors, then the result is another one of the integer’s factors. You divide an even integer x by 2. The quotient is a factor of x. Use the law of Syllogism to write the statement that follows from the pair of statements that are given.
  7. If Moose is hungry when he goes to the pizza shop, then he’ll finish a whole pizza. If Moose eats a whole pizza, then he goes through a pitcher of soda. If Moose is hungry when he goes to the pizza shop, then he drinks a pitcher of soda.
  8. If you mail the payment by noon, then it will arrive by tomorrow. If you payment arrives by tomorrow, then you won’t be charged a late fee. If you mail the payment by noon, then you won’t be charged a late fee.
  9. If Estelle takes her broker’s advice, she’ll invest in stock X. If Estelle invests in stock X, she’ll earn 50% on her investment by next year. If Estelle takes her broker’s advice, then she’ll earn 50% on her investment by next year.

20. If a triangle has two angles of 60 , then the triangle is equiangular. If a triangle is equiangular, then it

is also equilateral.

If a triangle has two angles of 60  , then it is also equilateral.

Decide whether the conclusion reached from the two statements demonstrates the Law of Detachment , the Law of Syllogism , or neither.

  1. If Cedric plays in a big game, then he gets nervous. If Cedric gets nervous, then he performs well. Conclusion: If Cedric plays in a big game, then he performs well. Law of Syllogism.
  2. If Leanne spends more than $30 on her car, then she’ll have to wait until next week to buy Michael’s birthday gift. Leanna spent $40 on her car. Conclusion: Leanne will have to wait until next week to buy Michael’s birthday gift. Law of Detachment
  3. If Lavonne gets money, she gives half of it to Sid. If Sid gets money, he gives half of it to Lavonne. Conclusion: Lavonne and Sid share their money equally. Neither.