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Zorluk: OrtaChaining Conditional Statements

Match each set of corporate policy premises with the logically valid deduction that can be derived by chaining them.

  • If a project undergoes an External Audit, it must receive Budget Approval. A project receives Budget Approval only if it passes the Compliance Review.If a project does not pass the Compliance Review, it does not undergo an External Audit.
  • The Director will Sign-off on a project whenever it passes the Compliance Review. Unless the Executive Board Reviews it, the Director will not Sign-off on the project.If the Executive Board does not Review a project, then it has not passed the Compliance Review.
  • Final Implementation occurs only if the Executive Board Reviews the project. If a project undergoes an External Audit, then Final Implementation will occur.Any project that undergoes an External Audit must be Reviewed by the Executive Board.
  • A project is Signed-off by the Director whenever it receives Budget Approval. Unless a project undergoes an External Audit, it will not be Signed-off by the Director.If a project does not undergo an External Audit, it does not receive Budget Approval.

Cevap

Set 1 pairs with the deduction about Compliance and Audit; Set 2 pairs with the deduction about Executive Board and Compliance; Set 3 pairs with the deduction about Audit and Executive Board; Set 4 pairs with the deduction about Audit and Budget.
Each premise set forms a transitive chain of conditionals (A -> B -> C), and the matching right item represents either the direct inference (A -> C) or its valid contrapositive (~C -> ~A).

Adım Adım Çözüm

1
Translate the premises of the first set into formal logic.
External Audit -> Budget Approval; Budget Approval -> Compliance Review.
Identifying the sufficient and necessary conditions allows us to form a logical chain.
2
Chain the premises of the first set and find the contrapositive.
Chain: External Audit -> Compliance Review. Contrapositive: ~Compliance Review -> ~External Audit.
This matches the right item stating 'If a project does not pass the Compliance Review, it does not undergo an External Audit.'
3
Translate the premises of the second set into formal logic.
Compliance Review -> Director Sign-off; Director Sign-off -> Executive Board Review.
'Whenever' introduces a sufficient condition. 'Unless X, not Y' translates to Y -> X.
4
Chain the premises of the second set and find the contrapositive.
Chain: Compliance Review -> Executive Board Review. Contrapositive: ~Executive Board Review -> ~Compliance Review.
This matches the right item stating 'If the Executive Board does not Review a project, then it has not passed the Compliance Review.'
5
Translate and chain the third set.
Final Implementation -> Executive Board Review; External Audit -> Final Implementation. Chain: External Audit -> Executive Board Review.
This directly matches the right item 'Any project that undergoes an External Audit must be Reviewed by the Executive Board.'
6
Translate and chain the fourth set.
Budget Approval -> Director Sign-off; Director Sign-off -> External Audit. Chain: Budget Approval -> External Audit. Contrapositive: ~External Audit -> ~Budget Approval.
This matches the right item stating 'If a project does not undergo an External Audit, it does not receive Budget Approval.'

Anahtar Kavram

Chaining Conditional Statements
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Konular

Chaining Conditional Statements

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