Syllogism Reasoning based questions

Question

Statements: Some G are I
Some H are I
Some H are M
No M is I
Conclusion: (1) All H being I is a possibility
(II) Some G are not M
(III) Some G being M is a possibility

Choose the one which matches/follows.

1. Only (i) and (iii) follow

2. Only (iii) follow

3. Only (i) and (ii) follow

Answer 1

Given Statements:

1. Some G are I

2. Some H are I

3. Some H are M

4. No M is I

Diagramming & Key Insights:

From Statement 4:
No M is I → There is a strict separation between sets M and I.

Now pair this with Statement 2:
Some H are I → So, those H elements that are I cannot be M, due to Statement 4.

Statement 3 says:
Some H are M → So, those H elements that are M cannot be I.

So, H is partly in I and partly in M, but the I part and M part cannot overlap.

Now, Evaluate Each Conclusion:

(I) All H being I is a possibility

• From earlier: Some H are M, and No M is I.

• So the part of H that is M can never be I.

• Therefore, entire H cannot be I.

• Conclusion (I) does NOT follow

(II) Some G are not M

• From the statements:
  We know Some G are I, and No M is I.
  So, those Gs that are I cannot be M.
  → Therefore, at least those Gs are not M.

• ✅ Conclusion (II) follows

(III) Some G being M is a possibility

• There is no statement connecting G and M directly or indirectly in a restrictive way.

• So, there’s no contradiction if some G is M.Conclusion (III) follows

Final Answer:

Only (II) and (III) follow

However, that option is not listed. Let's look at the options provided:

1. Only (I) and (III) follow ❌

2. Only (III) follow ❌

3. Only (I) and (II) follow ❌

None of the options match the correct answer (II and III).

So it seems like there may be a mistake in the options provided. If you're working from a printed source or a mock test, this might be a typo.