Two Statements are given followed by two Conclusions:
Statements:
The given statements assert that all numbers are divisible by 2 and by 3. When a number is divisible by two co-prime integers, it is also necessarily divisible by their product. Since 2 and 3 are co-prime numbers, any number divisible by both 2 and 3 must also be divisible by their product, which is 6. Therefore, Conclusion-I, stating that all numbers are divisible by 6, logically follows from the given statements.
Conclusion-II posits that all numbers are divisible by 4. The provided statements only establish divisibility by 2 and 3. Divisibility by 2 does not inherently imply divisibility by 4. For example, the number 6 is divisible by both 2 and 3, but it is not divisible by 4. Hence, Conclusion-II does not logically follow from the provided statements.
Options B, C, and D are incorrect because Conclusion-I is a valid inference, while Conclusion-II is not.