Question

Main statement: Only if the teaching standard is destroyed, will examination result be poor.

1. Examination result is poor.
2. Teaching standard is not destroyed.
3. Examination result is not poor.
4. Teaching standard is destroyed.

The ordered pair of statements is:
This questions has a main statement followed by four statements: 1, 2, 3, 4. Choose the ordered pair of statements where the first statement implies the second, and the two statements are logically consistent with the main statement.

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

Answer 1

The Correct Option is A

The correct option is (A): 2, 3.

Answer 2

The main statement, 'Only if the teaching standard is destroyed, will examination result be poor', is a conditional: it says a poor result can only happen when the teaching standard has been destroyed, in short, poor result implies destroyed standard. Its only valid twin, the contrapositive, is: standard not destroyed implies result not poor. Let's check each option against this:

1. 2, 3: 'Teaching standard is not destroyed' implying 'Examination result is not poor' is precisely the contrapositive of the main statement. If the standard was never destroyed, then, by the main statement's own logic, a poor result cannot have occurred. This pair holds up perfectly.
2. 2, 4: 'Teaching standard is not destroyed' implying 'Teaching standard is destroyed' directly contradicts itself, the same condition cannot both hold and not hold. This pair is invalid.
3. 1, 3: 'Examination result is poor' implying 'Examination result is not poor' is a straightforward self-contradiction as well. This pair is invalid.
4. 1, 2: 'Examination result is poor' implying 'Teaching standard is not destroyed' runs directly opposite to the main statement, which says a poor result requires the standard to be destroyed, not the reverse. This pair contradicts the main statement.

Only the pairing of 'standard not destroyed' leading to 'result not poor' reflects the logically necessary flip side of the original conditional.

Therefore, the correct answer is 2, 3.

Answer 3

Let P stand for "teaching standard is destroyed" and Q for "examination result is poor." The main statement, "Only if the teaching standard is destroyed, will examination result be poor," translates to Q implies P, a poor result can only happen when the standard is destroyed. In formal logic, the only statement guaranteed to follow from Q implies P is its contrapositive, not-P implies not-Q. Let's test each option against this:

1. 2, 3: Statement 2 is not-P, "teaching standard is not destroyed," and statement 3 is not-Q, "examination result is not poor." Not-P implies not-Q is exactly the contrapositive of Q implies P, so this pairing is logically guaranteed.
2. 2, 4: Statement 2 is not-P and statement 4 is P itself, claiming not-P implies P is a straightforward contradiction, never logically valid.
3. 1, 3: Statement 1 is Q and statement 3 is not-Q, claiming Q implies not-Q is also a direct self-contradiction.
4. 1, 2: Statement 1 is Q and statement 2 is not-P, claiming Q implies not-P reverses the main statement's actual direction, which says Q implies P, not the opposite.

Only the contrapositive pairing, not-P implies not-Q, follows validly from the main conditional Q implies P.

Therefore, the correct answer is 2, 3.