Answer
a) Modus Tollens
b) Disjunctive Syllogism
c) Universal Affirmative
d) Modus Tollens
e) Denying the Antecedent
f) Disjunctive Syllogism
Work Step by Step
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."
Conclusion:
From the premises, you can conclude that "I did not play hockey." This is derived using Modus Tollens, a valid form of conditional reasoning. Premise 3 negates the consequence "I am sore the next day" from premise 2, which allows you to conclude that the antecedent "I play hockey" is false.
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."
Conclusion:
From the premises, you can conclude that "I did not work last Monday." This conclusion is obtained using Disjunctive Syllogism, which allows you to infer the negation of one of the disjuncts when you know the negation of the other.
c)
"All insects have six legs."
"Dragonflies are insects."
"Spiders do not have six legs."
"Spiders eat dragonflies."
Conclusion:
From the premises, you can conclude that "Spiders are not insects." This conclusion follows from the Universal Affirmative rule, which states that if a characteristic is true for an entire class (insects), it is true for all individual members of that class (spiders not having six legs).
d)
"Every student has an Internet account."
"Homer does not have an Internet account."
"Maggie has an Internet account."
Conclusion:
From the premises, you can conclude that "Homer is not a student." This is derived using Modus Tollens. Premise 2 negates the consequence "Every student has an Internet account" from premise 1, allowing you to conclude that Homer is not a student.
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 are not healthy to eat."
Conclusion:
From the premises, you can conclude that "Tofu does not taste good." This conclusion follows from the Denying the Antecedent rule, which is a form of conditional reasoning. It allows you to infer the negation of the antecedent when the conditional statement is negated.
f)
"I am either dreaming or hallucinating."
"I am not dreaming."
"If I am hallucinating, I see elephants running down the road."
Conclusion:
From the premises, you can conclude that "I am hallucinating." This conclusion is derived from Disjunctive Syllogism. Since you know that "I am not dreaming" (premise 2), it allows you to infer that the remaining option, "I am hallucinating," is true.
