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Zorluk: OrtaMust Be True Questions

According to the regional agricultural board, any farmer in the valley who cultivates heirloom tomatoes must implement comprehensive pest-management protocols. Any farmer who implements comprehensive pest-management protocols is automatically disqualified from receiving the basic organic certification. Furthermore, recent records show that at least some farmers who received the newly established sustainability grant also qualified for the basic organic certification.

If the statements above are true, which one of the following must also be true?

  1. A
    Any farmer who is disqualified from receiving the basic organic certification cultivates heirloom tomatoes.
  2. B
    Most farmers who received the newly established sustainability grant do not implement comprehensive pest-management protocols.
  3. At least some farmers who received the newly established sustainability grant do not cultivate heirloom tomatoes.Cevap
  4. D
    Any farmer who does not cultivate heirloom tomatoes qualifies for the basic organic certification.
  5. E
    Comprehensive pest-management protocols are the most common reason that farmers in the valley are disqualified from receiving the basic organic certification.

Cevap

At least some farmers who received the newly established sustainability grant do not cultivate heirloom tomatoes.
The correct answer accurately combines the logical premises. First, we know that growing heirloom tomatoes requires comprehensive pest-management, which in turn prevents a farmer from getting the basic organic certification. Therefore, no farmer who grows heirloom tomatoes gets the certification. We also know that some farmers with the sustainability grant did get the certification. Because they got the certification, they cannot be farmers who grow heirloom tomatoes. Thus, at least some farmers with the grant do not cultivate heirloom tomatoes.

Adım Adım Çözüm

1
Diagram the first conditional statement.
Cultivates heirloom tomatoes (HT) -> Implement comprehensive pest-management (CPM).
To establish the baseline logical relationship for farmers growing heirloom tomatoes.
2
Diagram the second conditional statement and connect it to the first.
CPM -> Disqualified from basic organic certification (~BOC). Therefore, HT -> ~BOC.
Transitive property of conditional logic allows chaining statements with a shared term.
3
Diagram the third statement involving the quantifier 'some'.
Sustainability grant (SG) <-Some-> Qualifies for basic organic certification (BOC).
To integrate the quantified factual premise with the conditional chain.
4
Combine the 'some' statement with the contrapositive of the conditional chain.
Since SG <-Some-> BOC, and the contrapositive of the chain is BOC -> ~HT, it must be true that SG <-Some-> ~HT.
When 'Some A are B' and 'All B are C', it logically follows that 'Some A are C'.

Anahtar Kavram

Chaining Conditional Statements with Quantifiers
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