Question at position 21 Consider the following premises: P1: If a student passes the HSK Level 6 exam, then they can apply for graduate school in China. P2: If a student can apply for graduate school in China, then they may receive a scholarship. Which of the following statements necessarily follows from the premises?If a student receives a scholarship, they passed HSK Level 6.All students receive scholarships.No valid conclusion follows.If a student passes HSK Level 6, they may receive a scholarship.单项选择题
A
If a student receives a scholarship, they passed HSK Level 6.
B
All students receive scholarships.
C
No valid conclusion follows.
D
If a student passes HSK Level 6, they may receive a scholarship.

Question

Question at position 21 Consider the following premises: P1: If a student passes the HSK Level 6 exam, then they can apply for graduate school in China. P2: If a student can apply for graduate school in China, then they may receive a scholarship. Which of the following statements necessarily follows from the premises?If a student receives a scholarship, they passed HSK Level 6.All students receive scholarships.No valid conclusion follows.If a student passes HSK Level 6, they may receive a scholarship.单项选择题

A

If a student receives a scholarship, they passed HSK Level 6.

B

All students receive scholarships.

C

No valid conclusion follows.

D

If a student passes HSK Level 6, they may receive a scholarship.

BlackTom AI · Accepted Answer

From P1 and P2 we have a transitive implication: passing HSK Level 6 implies the ability to apply for graduate school in China, and that ability implies a possible scholarship.

1) Relevant knowledge points and concepts
- Material implication in logic: "If X then Y" is X → Y.
- Hypothetical syllogism (transitivity): If X → Y and Y → Z, then X → Z.
- Direction matters: A → B does not imply B → A.

2) Step-by-step reasoning
- Let A = "student passes HSK Level 6".
- Let B = "student can apply for graduate school in China".
- Let C = "student may receive a scholarship".
- P1 states A → B.
- P2 states B → C.
- By hypothetical syllogism, from A → B and B → C we conclude A → C.

3) Intermediate logical steps shown
- Assume A is true (a student passed HSK Level 6).
- From P1, derive B (they can apply for graduate school).
- From P2, derive C (they may receive a scholarship).
- Therefore whenever A holds, C follows; formally A → C.

4) Why the correct answer is correct
- The option "If a student passes HSK Level 6, they may receive a scholarship." is precisely A → C, which follows necessarily from the two premises by transitivity.

5) Why the other options are incorrect
- "If a student receives a scholarship, they passed HSK Level 6." (C → A) reverses the implication; the premises do not give this direction, so it does not follow.
- "All students receive scholarships." Overgeneralizes: premises only conditionally relate scholarship eligibility to passing HSK Level 6, not to every student.
- "No valid conclusion follows." False because A → C is a valid conclusion as shown.

6) Conclusion
- The necessary conclusion is "If a student passes HSK Level 6, they may receive a scholarship." This matches the provided correct answer.