Solution Found!
For each of these sets of premises, what relevant
Chapter 7, Problem 10E(choose chapter or problem)
For each of these sets of premises, what relevant conclusion or conclusions can be drawn? Explain the rules of inference used to obtain each conclusion from the premises.a) “If I play hockey, then I am sore the next day.” “I use the whirlpool if I am sore.” “I did not use the whirlpool.”________________b) “If I work, it is either sunny or partly sunny.” “I worked last Monday or I worked last Friday.” “It was not sunny on Tuesday.” “It was not partly sunny on Friday.”________________c) “All insects have six legs.” “Dragonflies are insects.” “Spiders do not have six legs.” “Spiders cat dragon-flies.”________________d) “Every student has an Internet account.” “Homer does not have an Internet account.” “Maggie has an Internet account.”________________e) “All foods that are healthy to eat do not taste good.” “Tofu is healthy to eat” “You only eat what tastes good.” “You do not eat tofu.” “Cheeseburgers arc not healthy to eat.”________________f) “I am either dreaming or hallucinating.” “I am not dreaming.” “If I am hallucinating, I see elephants running down the road”
Questions & Answers
QUESTION:
For each of these sets of premises, what relevant conclusion or conclusions can be drawn? Explain the rules of inference used to obtain each conclusion from the premises.a) “If I play hockey, then I am sore the next day.” “I use the whirlpool if I am sore.” “I did not use the whirlpool.”________________b) “If I work, it is either sunny or partly sunny.” “I worked last Monday or I worked last Friday.” “It was not sunny on Tuesday.” “It was not partly sunny on Friday.”________________c) “All insects have six legs.” “Dragonflies are insects.” “Spiders do not have six legs.” “Spiders cat dragon-flies.”________________d) “Every student has an Internet account.” “Homer does not have an Internet account.” “Maggie has an Internet account.”________________e) “All foods that are healthy to eat do not taste good.” “Tofu is healthy to eat” “You only eat what tastes good.” “You do not eat tofu.” “Cheeseburgers arc not healthy to eat.”________________f) “I am either dreaming or hallucinating.” “I am not dreaming.” “If I am hallucinating, I see elephants running down the road”
ANSWER:Solution:Step 1:a).Consider the following set of premises(properties):If i play hockey, then i am sore the next day.I use the whirlpool if i am sore.I did not use the whirlpoolSuppose that: i play hockey. i am sore. i use the whirlpool.Therefore the premises can be written as follows:If i play hockey, then i am sore the next day = I use the whirlpool if i am sore = I did not use the whirlpool = The following steps can be used to establish the conclusion from the above premises.Step Reasoni). Premise.ii). () Premiseiii). modus tollens from (i) and (ii)iv). () Premisev). () hypothetical syllogism (ii) and (iv)vi). modus tollens from (iii) and (iv)From the last step, it can be conclude that “i did not play hockey”.