Law of Detachment and Law of Syllogism

Law of Detachment and Law of Syllogism Use the Law of Detachment to determine the validity of each conjecture. If a conjecture is invalid provide a counterexample. 1. Given: If an animal is a cat, then it 2. Given: If an animal is a butterfly, 3. Given: If a toy is a Barbie Doll, has whiskers. Dora has whiskers. then it has wings. A Monarch is a then it has arms. Barbie has arms. type of butterfly. Conjecture: Dora is a cat. Conjecture: Barbie is a Barbie Conjecture: A Monarch has wings. Doll.

4. Given: If an object is a dresser, 5. Given: If an object is a piece of 6. Given: If Mark’s GPA is at least a then it has a drawer. The object has tape, then it is sticky. Monica has a 3.0, then he will take Driver’s Ed. a drawer. piece of tape. Mark has a GPA of 3.3. Conjecture: The object is a dresser. Conjecture: The tape is sticky Conjecture: Mark will take Driver’s Ed.

Use the Law of Syllogism to determine the validity of each conjecture. If a conjecture is invalid provide a counterexample. 7. Given: If today is Monday, then 8. Given: If Sara has surgery then she 9. Given: If Tom receives helium Jack will work. If Jack works, then will spend the next three days in balloons, then he will suck the he will earn money. Today is the hospital. If Sara spends the helium out of one. If it is Tom’s Monday next three days in the hospital then birthday then he will receive she will not attend school. Sara was helium balloons. Tom sucked Conjecture: Jack will earn money. not at school. helium out of a balloon. Conjecture: Sara had surgery. Conjecture: It is Tom’s birthday.

10. Given: If Darla is Mick’s date, 11. Given: If we go to grandma’s 12. Given: If Jesse passes all his then he will give Darla a corsage. If house then we will see our cousins. classes, then he will graduate from Mick goes to the prom, then he will If tomorrow is Thanksgiving, then high school. If Jesse graduates ask Darla to be his date. Darla has a we will go to grandma’s house. from high school, then he will get corsage. Tomorrow is Thanksgiving. his diploma. Jesse got his diploma.

Conjecture: Darla is Mick’s date Conjecture: We will see our Conjecture: Jesse passed all his for prom. cousins. classes.

Use the Law of Syllogism or Law of Detachment to write a valid conjecture. If no valid conjecture can be made, write not possible (NP). Remember if there is more than one if-then statement you should first try to use the Law of Syllogism. 13. If a fruit is a banana, then it has a peel. Jaime has a banana. 14. If I watch Fringe, then I will have popcorn. If tonight is Friday, then I will watch Fringe. Tonight is Friday. 15. If it is Halloween, then Rob and Wes will go trick or treating. If Rob and Wes go trick or treating, then they will wear a costume. It is Halloween. 16. If Wendy goes to the beach, then she will fly her kite. Wendy is at the beach. 17. Dan listens to music if he is studying. Dan is studying. 18. If Missy has an allergic reaction she will be rushed to the hospital. If Missy eats shellfish, she will have an allergic reaction. Missy was rushed to the hospital. 19. If Dumbo has his magic feather, then he can fly. Dumbo has his magic feather. 20. If an animal is a bat then it sees by echo-location. Freddy sees by echo-location.