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Difficulty: EasyDiagramming Conditional Statements

According to university policy, a student cannot register for the advanced robotics seminar unless they have completed the introductory physics course. Furthermore, no student can complete the introductory physics course without receiving a passing grade on the physics final exam.

Which of the following logically follows from the statements above?

  1. Any student who registers for the advanced robotics seminar has received a passing grade on the physics final exam.Answer
  2. B
    Any student who receives a passing grade on the physics final exam is allowed to register for the advanced robotics seminar.
  3. C
    A student who does not register for the advanced robotics seminar did not receive a passing grade on the physics final exam.
  4. D
    Any student who completes the introductory physics course will register for the advanced robotics seminar.
  5. E
    Most students who pass the physics final exam go on to register for the advanced robotics seminar.

Answer

Any student who registers for the advanced robotics seminar has received a passing grade on the physics final exam.
The stimulus provides two conditional rules that can be logically chained. The first rule, using the 'unless' indicator, translates to: If a student registers for the advanced seminar, they must have completed the introductory course. The second rule, using 'no... without', translates to: If a student completes the introductory course, they must have passed the final exam. Linking these (Register -> Complete -> Pass) yields the valid deduction that anyone who registers must have passed the final exam.

Step-by-Step Solution

1
Translate the first sentence into formal logic.
Register for Advanced Seminar -> Complete Introductory Course
The word 'unless' introduces a necessary condition. 'Cannot [X] unless [Y]' translates to 'If [X], then [Y]'.
2
Translate the second sentence into formal logic.
Complete Introductory Course -> Pass Final Exam
The phrase 'no... without' means the second part is necessary for the first. 'No [X] without [Y]' translates to 'If [X], then [Y]'.
3
Chain the conditional statements together.
Register for Advanced Seminar -> Complete Introductory Course -> Pass Final Exam
Because the necessary condition of the first statement matches the sufficient condition of the second statement, they can be linked transitively.
4
Derive the logical inference.
Register for Advanced Seminar -> Pass Final Exam
The transitive property of conditionals allows skipping the middle term to form a new valid conditional.

Key Concept

Diagramming Conditional Statements
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Topics

Diagramming Conditional Statements

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