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

Translate the main statement into logic
“Only if teaching standard is destroyed, examination result will be poor” means:
Poor result $\to$ Teaching destroyed.
Let $P =$ “Exam result is poor”, $D =$ “Teaching standard is destroyed”. Then the main statement is:
$P \to D$. Use the contrapositive
From $P \to D$ we get the logically equivalent contrapositive: $\neg D \to \neg P$. So the main statement allows two consistent conditionals:
- If results are poor, teaching must be destroyed. ($P \to D$)
- If teaching is not destroyed, results cannot be poor. ($\neg D \to \neg P$)
Test each ordered pair
(A) 2, 3: First is “Teaching standard is not destroyed” ($\neg D$). Second is “Exam result is not poor” ($\neg P$). From the contrapositive $\neg D \to \neg P$, statement 2 implies statement 3. Both are consistent with the main statement. Valid.
(B) 2, 4: $\neg D$ implies $D$? That would be a contradiction and not supported by the main statement. Invalid.
(C) 1, 3: $P$ implies $\neg P$? This is self-contradictory and does not follow from $P \to D$. Invalid.
(D) 1, 2: From the main statement, $P$ implies $D$, not $\neg D$. So $P \to \neg D$ contradicts the main statement. Invalid.
Conclusion
Only the pair (2, 3) satisfies “first implies second” while remaining consistent with the main statement.