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Geometry Syllogism & Detachment Problem Set Name

Determine if statement (3) follows from statements (1) and (2) by either Law of Detachment or the Law of Syllogism. If it does, write VALID. If it does not, write INVALID and give a counterexample.

1. (1) If a book is a biography, then it is nonfiction.

(2) You are reading a biography.

(3) It is nonfiction.

2. (1) If you wear the school colors, then you have school spirit.

(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 eat too much turkey, then you will get sick.

(2) Kelly got sick.

(3) Kelly ate too much turkey.

4. (1) If you order the apple pie, then it will be served with ice cream.

(2) Matt ordered the apple pie.

(3) Matt was served ice cream.

5. (1) If I eat my dinner, then I will get popcorn for desert.

(2) If I eat popcorn for desert, then I’ll need to floss.

(3) If I floss, then I had popcorn for desert.

Determine if a conclusion can be made from each set of statements. If possible, write the conclusion. If not possible, write “INVALID” and explain why.

6. If two lines have equal slopes, then the lines are parallel.

If the lines are parallel, then the lines do not intersect.

Conclusion:

7. If today is Saturday then there is no school.

There was no school today.

Conclusion:

8. If today is Election Day, then there is no school.

If there is no school, then I will sleep in late.

Conclusion:

9. If angle A and angle B are right angles, then the angles are congruent.

Angle A and angle B are right angles.

Conclusion:

Use inductive or deductive reasoning to reach a valid conclusion.

10. For the past three Wednesdays, the cafeteria has served burritos for lunch. Jack concludes…

11. Julie knows that American Eagle jeans cost less than Nordstrom jeans. All other jeans that Julie knows of cost less than American Eagle jeans. Julie reasons...

12. If you live in Virginia and are between the ages of 16 and 18, then you must take driver’s education to get your license. Tony lives in Virginia, is 16 years old, and has his driver’s license. Therefore, Tony …

State whether the argument is valid. Explain your reasoning.

13. Jeff knows that if he does not do his chores in the morning, he will not be allowed to play video games later the same day. Jeff does not play video games on Saturday afternoon. So Jeff did not do his chores on Saturday morning.

14. Katie knows that all sophomores take drivers education in her school. Brandon takes driver education. So Brandon is a sophomore.

15. Write your own argument using the Law of Syllogism.

16. Write you own argument using the Law of Detachment.

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