Syllogisms & Logic

1. All zebras are striped animals.
   No zebras are polar bears.
   Therefore, no polar bears are striped animals. * Valid: All premises are true. Conclusion follows from them.
   
   2. All clowns are funny individuals.
   Some sad people are clowns.
   Therefore, some sad people are funny individuals.

* Invalid: Not all premises are true. Conclusion does not follow from them – even if they were all true, the conclusion wouldn’t have to.

3. Some sticky substances are yucky things.
All taffy is a sticky substance.
Therefore, some taffy is a yucky thing.
* Invalid: Not all premises are true. Conclusion does follow from them, though.

4. All items made of gold are expensive items.
Some rings are items made of gold.
Therefore, some rings are expensive items.
* Valid: All premises are true. Conclusion follows from them.

5. All flies are winged creatures.
All butterflies are winged creatures.
Therefore, all butterflies are flies.

* Invalid: All premises are true. Conclusion, however, does not follow from them.

6. All fragile things are breakable things.
Some glasses are fragile things.
Therefore, some glasses are breakable things.

7. All mammals are warm-blooded animals.
All whales are mammals.
Therefore, all whales are warm-blooded animals.

8. All books are things with pages.
Some books are mysteries.
Therefore, some pages are mysteries.

9. All flowers are pretty objects.
All pansies are flowers.
Therefore, all pansies are pretty objects.

10. No animals are plants.
All sheep are animals.
Therefore, no sheep are plants.

11. Madeline must have known the material for the test, because if a person knows the material, that person will get an A, and Madeline was one of the students that got an A.

Form:  1. K → G

2. G
3. K                                                         * invalid [affirming the consequent]
4. Anastasia believes that if she treats people honestly and with an open mind, she will have diverse friendships. She is honest and open-minded and has friends all over the world.

Form:  1. H → D

2. H
3. D * valid modus ponens [affirming the antecedent]
4. Roberto thought that if he worked very hard, his boss would give him a raise or a promotion. He made sure she noticed him, but she did not give him a raise or promotion. He thought he must not have worked hard enough.

Form:  1. W → G

2. ~G
3. ~W * valid modus tollens [denying the consequent]

   14. I’m still eating too much ice cream, lamented George. My waist measurement is the same as it was six months ago. I know if I didn’t eat so much ice cream, I would reduce my waist   size.

Form:  1. ~E → R

2. E
3. ~R                            * invalid [denying the antecedent]

   15. The best way to make sure we pay fewer taxes is to elect conservatives. We must not have elected enough conservatives, because we are paying more taxes.

Form:  1. E → P

2. ~P
3. ~E                 * valid modus tollens [denying the consequent]

   16. If my neighbor were a decent human being, he wouldn’t let his yard trash fall onto my property. But he’s not a decent human being, so we get to clean his trash as well as ours.

Form:  1. D → ~T

2. ~D
3. T     * invalid [denying the antecedent]

   17. We’ll have fun and learn a lot in this course, if we have great facilitator. We do have a great facilitator; therefore we are learning a lot and having fun doing it!

Form:  1. G → F

2. G
3. F * valid modus ponens [affirming the antecedent]

   18. If I could understand the concept of hypothetical syllogisms, I would get a passing grade. Hurray! I got a passing grade, so I must have understood the concept of hypothetical syllogisms.

Form:  1. U → P

2. P
3. U                                                     * invalid [affirming the consequent] 

 

 

Reference:

Gustason, W., & Ulrich, D. E. (1989). Elementary Symbolic Logic (2nd ed.): Waveland Press, Inc.