Question

Choose the ordered pair of statements where the first statement implies the second, and the two statements are logically consistent with the main statement.

Main statement: Only if the teaching standard is destroyed, will examination result be poor.
Statements: 
1. Examination result is poor. 
2. Teaching standard is not destroyed. 
3. Examination result is not poor. 
4. Teaching standard is destroyed. 
Choose the ordered pair in which the first statement implies the second, and both are logically consistent with the main statement.

• A. 2, 3
• B. 2, 4
• C. 1, 3
• D. 1, 2

Hint:

“Only if $Q$ then $P$” translates to $P \to Q$. Always write its contrapositive $\neg Q \to \neg P$—it often unlocks the correct option in implication questions.

Answer 1

The Correct Option is A

The key fact from "only if the teaching standard is destroyed will the result be poor" is that a poor result and an intact teaching standard can never occur together.

1. 2, 3: if the teaching standard is not destroyed, the result cannot be poor, so it must be "not poor", this pair holds up.
2. 2, 4: claims not destroyed leads to destroyed, a plain contradiction.
3. 1, 3: claims poor leads to not poor, also a contradiction between the two statements themselves.
4. 1, 2: a poor result actually points to the teaching standard being destroyed, not intact, so this pair reverses the true relationship.

Since only 2, 3 stays free of contradiction and matches the main statement, the correct answer is 2, 3.

Answer 2

The main statement blocks exactly one combination of the two ideas: a poor result occurring while the teaching standard stays intact. Every other combination is allowed, teaching destroyed with a poor result, teaching destroyed with a result that isn't poor, and teaching not destroyed with a result that isn't poor. Let's check each pair against this list of allowed combinations.

1. 2, 3 (not destroyed, not poor): matches one of the allowed combinations exactly, so the first statement being true is consistent with, and forces, the second.
2. 2, 4 (not destroyed, destroyed): these two statements can't both describe the same situation, so this pair fails before the allowed list is even needed.
3. 1, 3 (poor, not poor): also two statements that contradict each other directly, regardless of the main statement.
4. 1, 2 (poor, not destroyed): describes the one forbidden combination, a poor result with teaching not destroyed, so it goes directly against the main statement rather than following from it.

Since 2, 3 is the only pair that lines up with an allowed combination, the correct answer is 2, 3.