Statements: Some saints are balls. All balls are bats. Some tigers are balls.…

When two premises share a common (middle) term, a particular affirmative statement ("Some X are M") combined with a universal affirmative statement ("All M are Y") yields a particular conclusion in the remaining terms ("Some X are Y") — never a universal one. Separately, a particular affirmative statement converts simply: "Some X are Y" also means "Some Y are X". A universal affirmative, however, converts only to a particular: "All X are Y" licenses just "Some Y are X", never "All Y are X".

1. "Some saints are balls" and "All balls are bats" share the middle term "balls"; combining them gives "Some saints are bats" — exactly Conclusion II, so II follows.

2. "Some tigers are balls" and "All balls are bats" also share the middle term "balls"; combining them gives "Some tigers are bats".

3. Since "Some tigers are bats" is a particular affirmative statement, it converts simply to "Some bats are tigers" — exactly Conclusion I, so I follows too.

4. Conclusion III, "All bats are balls," would require reversing the universal premise "All balls are bats" into another universal statement; the conversion rule for a universal affirmative permits only a particular reversal ("Some bats are balls"), never a full universal reversal — so III does not follow.

A quick set check confirms this: "All balls are bats" places the entire balls-set inside the bats-set, so any saint or tiger that is also a ball must be a bat — this backs both particular conclusions above. But nothing in the premises stops the bats-set from extending beyond the balls-set, so the bats-set need not sit entirely inside the balls-set — confirming the universal reversal in Conclusion III is unwarranted.

So exactly Conclusions I and II follow.