Answer :

Solution :

Based on the given statements, we can make the following logical inferences:

Inference 1: If (i) is true and (ii) is true, then (iii) is true. If there exists at least one rose that is red (i) and all red flowers fade quickly (ii), then it is implied that there exists at least one rose that fades quickly (iii). This inference is valid because the conditions in (i) and (ii) are fulfilled.

Inference 2: If (i) is true and (ii) is false, then (iii) is true. If there exists at least one rose that is red (i) and not all red flowers fade quickly (ii), then it is still possible for there to exist at least one rose that fades quickly (iii). This inference is valid because the conditions in (i) are fulfilled, and the condition in (ii) does not contradict the possibility of (iii).

Inference 3: If (i) is false and (ii) is true, then (iii) is false. If there are no roses that are red (i) and all red flowers fade quickly (ii), then it is not possible for there to exist any rose that fades quickly (iii). This inference is valid because the condition in (ii) implies that only red flowers fade quickly, and if there are no red roses, then there are no roses that fade quickly.

Inference 4: If (i) is false and (ii) is false, then (iii) is false. If there are no roses that are red (i) and not all red flowers fade quickly (ii), then it is not possible for there to exist any rose that fades quickly (iii). This inference is valid because the condition in (ii) does not imply that all roses fade quickly, and the condition in (i) implies that there are no red roses.

Conclusion: Based on the logical inferences, we can conclude that if both (i) and (ii) are true, then (iii) is true. Hence, option 'C' is the correct answer.