Identify the correct code on the basis of the following argument:
All actors are athletes.
Some actors are comedians.
Therefore, some comedians are athletes.

Correct option is C

Introduction:

A syllogism is a logical argument that uses two premises to draw a conclusion. Each statement has three terms — Major (P), Minor (S), and Middle (M) — and the structure (arrangement of these terms) determines the figure of the syllogism.

Information Booster:

• Additional Information:

  1. Translate statements into categorical form

  • Mood letters meaning:

    • A: Universal Affirmative (All M are P)

    • I: Particular Affirmative (Some S are M / Some S are P)

  • Darii (AII–1) is one of the valid moods of Aristotelian syllogisms.

  • Other valid moods in Figure 1 include:

    • AAA–1 (Barbara)

    • EAE–1 (Celarent)

    • AII–1 (Darii)

    • EIO–1 (Ferio)

  1. "All actors are athletes"

     • Subject: actors (S)

     • Predicate: athletes (P)

     • Form: All S are P → A proposition (Universal Affirmative)

  2. "Some actors are comedians"

     • Subject: actors (S)

     • Predicate: comedians (M)

     • Form: Some S are M → I proposition (Particular Affirmative)

  3. Conclusion: "Some comedians are athletes"

     • Subject: comedians (M)

     • Predicate: athletes (P)

     • Form: Some M are P → I proposition

So the argument form is:

• Premise 1: A (S, P)

• Premise 2: I (S, M)

• Conclusion: I (M, P)

2. Identify the Figure

The Figure depends on the position of the middle term (actors = S) in the premises.

• Premise 1: S–P (Middle term = Subject in first premise)

• Premise 2: S–M (Middle term = Subject in second premise)

That means the middle term is subject in both premises — unusual for valid syllogisms, but let's check the figure definition:

Figure is determined by the position of the middle term in the two premises:

• 1st Figure: M–P, S–M

• 2nd Figure: P–M, S–M

• 3rd Figure: M–P, M–S

• 4th Figure: P–M, M–S

But here we have:
Premise 1: S–P
Premise 2: S–M

We can rearrange premise order to fit standard form (major premise first: P related to M; minor premise: S related to M).

But in our case:

• Major term (P) = athletes (predicate of conclusion)

• Minor term (M) = comedians (subject of conclusion)

• Middle term (S) = actors

Conclusion: Some M are P.

So:
Major premise: should contain P.
Minor premise: should contain S (minor term) and middle term.

But wait — our given premises:

1. All S are P (middle = S, major = P)

2. Some S are M (middle = S, minor = M)

This is actually:
Middle term = S (actors)
Major term = P (athletes)
Minor term = M (comedians)

So:
Premise 1: Middle–Major (S–P)
Premise 2: Middle–Minor (S–M)

That’s Figure 3 (M–P, M–S) if we swap the order of premises? Let's align:

Standard form for Figure 3:
Premise 1: M–P
Premise 2: M–S
Conclusion: S–P

But our conclusion is M–P (Some comedians are athletes), so S = comedians? No — careful:

Let’s reassign:
Let

• M = actors (middle term)

• S = comedians (minor term)

• P = athletes (major term)

Then:
Premise 1: All M are P (All actors are athletes) → M–P
Premise 2: Some M are S (Some actors are comedians) → M–S
Conclusion: Some S are P (Some comedians are athletes) → S–P

That’s exactly Figure 3:
M–P
M–S
∴ S–P

3. Mood

Mood = types of propositions in order:
Premise 1: A (M–P)
Premise 2: I (M–S)
Conclusion: I (S–P)

So mood = AII

4. Check validity

Figure 3, Mood AII (Darapti) — in traditional logic (assuming existential import), this is valid.
In modern logic, without existential import, it’s invalid if "actors" is empty, but here we have "Some actors are comedians" which guarantees M is non-empty, so it’s valid.

5. Match with options

The options given:

• AII; Ist Figure

• AIA; IInd Figure

• AII; IIIrd Figure

• IAI; IVth Figure

We have AII; 3rd Figure

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