Answer
a) Modus Tollens
b) Modus Tollens
c) Disjunctive Syllogism
d) Modus Tollens
e) Hypothetical Syllogism
f) Universal Affirmative
Work Step by Step
a)
"If I take the day off, it either rains or snows."
"I took Tuesday off or I took Thursday off."
"It was sunny on Tuesday."
"It did not snow on Thursday."
Conclusion:
Based on the premises, you can conclude that "I did not take Tuesday off." This is obtained using the rule of Modus Tollens, which is a valid form of conditional reasoning. Starting with premise 2, you can infer that "I did not take Tuesday off" because the condition "It was sunny on Tuesday" (premise 3) negates the consequence "It either rains or snows" (premise 1).
b)
"If I eat spicy foods, then I have strange dreams."
"I have strange dreams if there is thunder while I sleep."
"I did not have strange dreams."
Conclusion:
Based on the premises, you can conclude that "I did not eat spicy foods." This conclusion is derived using Modus Tollens. Premise 3 negates the consequence "I have strange dreams" from premise 2, which allows you to conclude that the antecedent "I eat spicy foods" is false.
c)
"I am either clever or lucky."
"I am not lucky."
"If I am lucky, then I will win the lottery."
Conclusion:
Based on the premises, you can conclude that "I am clever." This conclusion follows from the Disjunctive Syllogism, which states that if you have a disjunction (either A or B) and you know that one of the disjuncts (B) is false, you can infer the truth of the other disjunct (A).
d)
"Every computer science major has a personal computer."
"Ralph does not have a personal computer."
"Ann has a personal computer."
Conclusion:
From the premises, you can conclude that "Ralph is not a computer science major." This is derived using Modus Tollens. Premise 2 negates the consequence "Every computer science major has a personal computer" from premise 1, which allows you to conclude that Ralph is not a computer science major.
e)
"What is good for corporations is good for the United States."
"What is good for the United States is good for you."
"What is good for corporations is for you to buy lots of stuff."
Conclusion:
Based on the premises, you can conclude that "Buying lots of stuff is good for you." This conclusion is obtained using Hypothetical Syllogism, which allows you to chain multiple conditional statements together to derive a conclusion.
f)
"All rodents gnaw their food."
"Mice are rodents."
"Rabbits do not gnaw their food."
"Bats are not rodents."
Conclusion:
From the premises, you can conclude that "Bats do not gnaw their food." This conclusion is a straightforward application of the Universal Affirmative rule, which states that if a characteristic is true for an entire class (in this case, all rodents), it is true for all individual members of that class (bats being non-rodents
