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Difficulty: EasyStatement and Conclusions or Inferences

Review the rules and outcomes concerning the rural development program below:

1. To be eligible for the grant, a municipality must have fewer than 5,000 residents and an active water conservation board.
2. The municipality of Palanpur successfully secured the grant this year.

Based strictly on the provided facts, which of the following conclusions are logically valid? (Select all that apply)

  1. The municipality of Palanpur has an active water conservation board.Answer
  2. B
    Any municipality with fewer than 5,000 residents will automatically secure the grant.
  3. The municipality of Palanpur has fewer than 5,000 residents.Answer
  4. D
    The grant is exclusively given to the municipality of Palanpur this year.

Answer

The valid conclusions are that Palanpur has an active water conservation board and that it has fewer than 5,000 residents.
The correct conclusions rely entirely on direct deduction. The statements establish a rule where receiving a grant requires two specific conditions to be met. Because Palanpur received the grant, it is an absolute logical certainty that Palanpur meets both of these mandated conditions.

Step-by-Step Solution

1
Analyze the conditions required to receive the grant.
Two necessary conditions are identified: population under 5,000 AND an active water conservation board.
To accurately deduce facts about grant recipients, all eligibility rules must be clearly understood.
2
Apply the outcome of the second statement to the conditions from the first statement.
Since Palanpur received the grant, it must satisfy all necessary conditions.
Logically, if a result has occurred, all mandatory prerequisites for that result must have been met.
3
Evaluate each conclusion against the derived facts.
Conclusions stating Palanpur meets the two specific requirements are valid. Conclusions adding extreme modifiers ('exclusively') or misinterpreting the requirements ('automatically secure') are invalid.
Direct inferences must not add external assumptions or distort the original scope of the statements.

Key Concept

Direct Logical Deduction from Conditional Statements
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Topics

Statement and Conclusions or Inferences

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