The question goes like this:
Ms. Li has just moved into a new home and plans to buy several potted plants at once. Her thoughts are as follows:
Buy either Green Radish or Podocarpus.
Buy at least one of Spider Plant, Green Radish, and Rubber Tree.
Buy at least two of Podocarpus, Rubber Tree, and Sansevieria.
If Podocarpus is bought, then Spider Plant is not bought.
If all the above conditions are met,
then Which of the following options A, B, C, D is necessarily correct?:
A. Ms. Li bought Sansevieria.
B. Ms. Li bought Rubber Tree.
C. Ms. Li bought either Podocarpus or Spider Plant.
D. Ms. Li bought at least three kinds of potted plants.
The reasoning goes like this:
The question asks which option is necessarily correct, and one approach is to start from a modus tollens reasoning.
The only if-then statement in the question is sentence 4: If Podocarpus is bought, then Spider Plant is not bought.
From sentence 1, we can derive that if Podocarpus is bought, then Green Radish is not bought either.
Combining these two conditions, we can conclude that if Podocarpus is bought, then both Spider Plant and Green Radish are not bought, which leads to the necessity of buying Rubber Tree.
From sentence 3, if Podocarpus is not bought, then Rubber Tree and Sansevieria must be bought.
Therefore, whether Podocarpus is bought or not, Rubber Tree must be bought. The answer is B.
Reduceand simplify usingBooleanMinimizeonce statements have been coded. If it is a question about natural language processing: I defer to others. $\endgroup$BooleanMinimize[{G ⊻ P && S ∨ G ∨ R && (P ∧ R ) ∨ (P ∧ S) ∨ (R ∧ S) && P \[Implies] ¬ S}]gives{(! G && ! P) || ! S}$\endgroup$