Examkin

Question

Difficulty: MediumChaining Conditional Statements

Pair each set of operational spacecraft protocols with the logically valid deduction that can be correctly chained from its premises.

  • If the probe enters the atmosphere, the heat shield deploys. If the heat shield deploys, telemetry data is transmitted.If the probe enters the atmosphere, telemetry data is transmitted.
  • The probe enters the atmosphere only if the solar panels retract. Telemetry data is transmitted only if the solar panels do not retract.If telemetry data is transmitted, the probe does not enter the atmosphere.
  • Unless the primary engine fires, the orbit will not stabilize. Telemetry data is transmitted only if the orbit stabilizes.If telemetry data is transmitted, the primary engine fires.
  • If the backup battery engages, the primary engine fires. The orbit stabilizes only if the primary engine does not fire.If the orbit stabilizes, the backup battery does not engage.

Answer

Each premise set must be translated into formal if-then logic to locate the shared term. By applying contrapositives where necessary, you can form a continuous transitive chain (A -> B -> C) to reach the required conclusion.
The correct pairings successfully utilize formal logic rules, particularly the contrapositive, to link the sufficient condition of one premise to the necessary condition of the second, resulting in an unassailable deduction.

Step-by-Step Solution

1
Translate each statement into formal conditional logic, paying close attention to indicator words like 'if', 'only if', and 'unless'.
You produce a set of logical relationships, such as A -> B and C -> Not B.
Standardizing the language allows you to see the logical flow without getting distracted by the narrative context.
2
Identify the shared variable between the two conditional statements.
You isolate the term that will act as the bridge in the deductive chain.
A chain can only be formed if the necessary condition of one statement matches the sufficient condition of another.
3
Apply the contrapositive to one of the statements if the shared variable has a mismatched polarity (e.g., B in one statement, Not B in the other).
The statements align cleanly (e.g., C -> Not B, and Not B -> Not A).
The contrapositive preserves the original truth value while rearranging the terms to enable transitive linking.
4
Follow the transitive property from the first sufficient condition to the final necessary condition.
You formulate the final valid deduction (e.g., C -> Not A).
This guarantees the final inference must logically be true based on the initial premises.

Key Concept

Chaining Conditional Statements
Rate this question

Topics

Chaining Conditional Statements

More questions from this topic