Given below are two statements: Statement I: Some examinations are too long.…
2020
Given below are two statements: Statement I: Some examinations are too long. Some examinations are too difficult. Therefore, some examinations are too long and too difficult.
Statement II: Some dogs chase cats. All dogs have fleas. Therefore, some cat-chasing dogs have fleas.
In the light of the above statements, choose the correct answer from the options given below:
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is correct but Statement II is false
- D.
Statement I is incorrect but Statement II is true
Attempted by 11 students.
Show answer & explanation
Correct answer: D
Concept
An argument is valid only when its conclusion MUST be true whenever all its premises are true — validity is about the logical form, not whether the sentences sound reasonable. Two particular ('Some') premises about the same subject cannot be combined into a single 'Some ... and ...' claim, because the things that satisfy one premise need not be the same things that satisfy the other (the fallacy of illicit combination / undistributed middle).
Applying it to Statement I
Statement I argues: Some examinations are long; some examinations are difficult; therefore some examinations are long AND difficult.
'Some examinations are long' identifies one (possibly entire) subset of exams that are long.
'Some examinations are difficult' identifies another subset that are difficult.
Nothing guarantees these two subsets overlap — the long exams could be completely different exams from the difficult ones.
So the conclusion 'some are long AND difficult' does not follow from the premises; the form is invalid.
Hence Statement I is an INVALID argument (incorrect).
Applying it to Statement II
Statement II argues: Some dogs chase cats; all dogs have fleas; therefore some cat-chasing dogs have fleas.
'Some dogs chase cats' guarantees at least one cat-chasing dog exists; every such dog is a dog.
'All dogs have fleas' is a universal premise covering every dog, including each cat-chasing dog.
Therefore each cat-chasing dog must have fleas, so 'some cat-chasing dogs have fleas' is forced by the premises.
The form is valid (a particular premise plus a universal premise yields the particular conclusion).
Hence Statement II is a VALID argument (true/correct).
Cross-check
Combining the two findings: one argument's conclusion is not forced by its premises (its form fails), while the other's conclusion is genuinely compelled by a universal premise applied to a case that must exist. So one statement's reasoning is incorrect and the other's is correct, which selects the pairing 'one statement incorrect, the other true'.