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Zorluk: Çok zorMust Be True / Most Strongly Supported

The faculty senate at a research university recently adopted new bylaws governing research funding. The bylaws stipulate that any grant proposal involving human subjects must be reviewed by the ethics board unless the proposal is exclusively funded by an internal departmental budget. Furthermore, no proposal that is reviewed by the ethics board can be approved for expedited processing. Every proposal that is exclusively funded by an internal departmental budget is exempt from the standard peer-review process.

Based on these bylaws, it must be true that if a grant proposal involving human subjects is approved for expedited processing, it is exempt from the standard peer-review process.

Cevap: Cevap

Cevap

True
The statement is logically guaranteed by chaining the contrapositive of the expedited processing rule through the 'unless' exception of the human subjects rule, ultimately triggering the peer-review exemption.

Adım Adım Çözüm

1
Translate the premises into formal conditional statements.
Premise 1: Human Subjects → (Ethics Board OR Exclusively Internal). Premise 2: Ethics Board → NOT Expedited. Premise 3: Exclusively Internal → Exempt from Peer Review.
Formalizing the rules prevents misinterpretation of complex logical operators, particularly the word 'unless'.
2
Analyze the conditions provided in the statement to be evaluated.
The statement proposes a specific scenario: a grant proposal has both Human Subjects (HS) and Expedited Processing (EXP).
These act as sufficient conditions from which we must derive the necessary outcome to test the statement.
3
Apply the contrapositive of Premise 2 to the Expedited condition.
Premise 2 states: Ethics Board → NOT Expedited. The contrapositive is: Expedited → NOT Ethics Board. Therefore, this proposal was NOT reviewed by the Ethics Board.
We must follow the logical chain backward from the known outcome (Expedited Processing).
4
Evaluate Premise 1 using the deduced information.
Premise 1 requires Human Subjects proposals to go to the Ethics Board UNLESS they are Exclusively Internal. Since our proposal bypassed the Ethics Board, it must trigger the exception: it is Exclusively Internal.
In a necessary condition involving a disjunction (A or B), if one option (A) is eliminated, the other (B) must be true.
5
Apply the deduction from Step 4 to Premise 3.
Since the proposal is Exclusively Internal, Premise 3 dictates it is Exempt from Peer Review. This matches the outcome predicted by the statement perfectly.
This completes the logical chain from the initial conditions to the required outcome, proving the statement must be true.

Anahtar Kavram

Formal Logic, Conditional Chaining, and Contrapositives
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Konular

Must Be True / Most Strongly Supported

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