Syllogism – Chain reasoning with “all” and “some” Statements: • Some saints are balls. • All balls are bats. • Some tigers are balls. Conclusions to test: I. Some bats are tigers. II. Some saints are bats. III. All bats are balls.

Introduction / Context:
This item combines universal inclusion (“all balls are bats”) with existential overlaps (“some saints/tigers are balls”). The goal is to propagate membership through the universal set while testing which categorical conversions are valid.

Given Data / Assumptions:

• Some saints are balls (S ∩ B ≠ ∅).
• All balls are bats (B ⊆ Bt).
• Some tigers are balls (T ∩ B ≠ ∅).

Concept / Approach:
If a particular element lies in “balls,” and “all balls are bats,” then that element automatically lies in “bats.” Therefore, any “some … are balls” statement converts into “some … are bats.” Conversely, “all bats are balls” is not supported by “all balls are bats” (that would be the illicit converse of a universal statement).

Step-by-Step Solution:
I. Some bats are tigers: Since some tigers are balls and every ball is a bat, those same tigers are bats. Hence I follows.II. Some saints are bats: Since some saints are balls and all balls are bats, those same saints are bats. Hence II follows.III. All bats are balls: The given universal is one-way (balls ⊆ bats). It does not establish the reverse (bats ⊆ balls). III does not follow.

Verification / Alternative check:
Imagine bats include many things besides balls; the premises remain true while III fails. I and II must hold due to direct subset propagation from B to Bt.

Why Other Options Are Wrong:

• Options including III accept an illicit converse.
• “Only II follows” ignores the equally valid propagation for tigers.
• “None of these” is incorrect because I and II are compelled.

Common Pitfalls:
Conflating “all A are B” with “all B are A”; forgetting that “some A are B” can be pushed through a universal inclusion.

Final Answer:
Only I and II follow