Question

Statements:
1. All engineers are intelligent.
2. Some intelligent people are lazy.
Conclusions:
I. Some engineers are lazy.
II. All intelligent people are engineers.
Choose the correct option:

• A. Only I follows
• B. Only II follows
• C. Neither I nor II follows
• D. Both I and II follow

Hint:

• Statement 1 (All A are B) Draw set A entirely within set B.
• Statement 2 (Some B are C) Draw set C overlapping with set B.
• Conclusion I (Some A are C) Check if the overlap between B and C *must* also overlap with A. It is not guaranteed. The overlap might be in the part of B that is not A.
• Conclusion II (All B are A) This is the converse of "All A are B" and is not implied by it unless A and B are identical sets.
• Venn diagrams are very helpful for these types of syllogism problems.

Answer 1

The Correct Option is C

Let E represent the set of engineers, I represent the set of intelligent people, and L represent the set of lazy people.
Statement 1: All engineers are intelligent. This implies that E is a subset of I (E $\subseteq$ I).
Statement 2: Some intelligent people are lazy. This implies that the intersection of I and L is non-empty (I $\cap$ L $eq \emptyset$).

Conclusion I: Some engineers are lazy. (Is E $\cap$ L $eq \emptyset$?)
Given E $\subseteq$ I and I $\cap$ L $eq \emptyset$.
Using a Venn diagram, E is fully contained within I. L overlaps with I.
This overlap between I and L could be outside of E, or it could intersect with E.
Example:
Intelligent people = {i1, i2, i3, i4, i5}
Engineers = {i1, i2} (satisfies Statement 1)
Lazy people = {i3, i4} (satisfies Statement 2, as i3 and i4 are intelligent and lazy)
In this example, no engineer is lazy. Therefore, "Some engineers are lazy" is not necessarily true. Conclusion I does not logically follow.

Conclusion II: All intelligent people are engineers. (Is I $\subseteq$ E?)
Statement 1, E $\subseteq$ I, means all engineers are intelligent, but it does not mean all intelligent people are engineers. Intelligent individuals who are not engineers can exist.
Example: Intelligent people = {i1, i2, i3}. Engineers = {i1, i2}. Here, i3 is intelligent but not an engineer.
Therefore, Conclusion II does not logically follow.

Since neither Conclusion I nor Conclusion II necessarily follows from the given statements, the correct option is (c).
\[ \boxed{\text{Neither I nor II follows}} \]