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 = set of engineers, I = set of intelligent people, L = set of lazy people.
Statement 1: All engineers are intelligent. This means E is a subset of I (E $\subseteq$ I).
Statement 2: Some intelligent people are lazy. This means there is a non-empty intersection between I and L (I $\cap$ L $\neq \emptyset$).
Conclusion I: Some engineers are lazy. (E $\cap$ L $\neq \emptyset$?) From E $\subseteq$ I and I $\cap$ L $\neq \emptyset$.
Consider a Venn diagram. The set E is entirely within I. The set L overlaps with I.
The overlap between I and L could be entirely outside of E, or it could overlap with E.
Example:
Intelligent people = {i1, i2, i3, i4, i5}
Engineers = {i1, i2} (all engineers are intelligent)
Lazy people = {i3, i4} (some intelligent people are lazy; here i3, i4 are intelligent and lazy)
In this example, no engineer is lazy. So, "Some engineers are lazy" is not necessarily true. Conclusion I does not follow.
Conclusion II: All intelligent people are engineers. (I $\subseteq$ E?)
Statement 1 says E $\subseteq$ I. This means all engineers are intelligent, but it does not imply the converse that all intelligent people must be engineers. There can be intelligent people who are not engineers.
Example: Intelligent people = {i1, i2, i3}. Engineers = {i1, i2}. Here, i3 is intelligent but not an engineer.
So, Conclusion II does not follow.
Since neither Conclusion I nor Conclusion II necessarily follows from the statements, the correct option is (c).
\[ \boxed{\text{Neither I nor II follows}} \]