Consider the following phrase: Statements: All mangoes are bananas. Some…

Concept: When two conclusions on the same pair of terms are complementary — one says 'Some X are Y' and the other says 'No X is Y' — together they cover every possible relationship between X and Y (there either is some overlap or there is none). If neither statement follows with certainty on its own, but at least one valid diagram supports each of the two separately, the correct reading is 'Either conclusion I or conclusion II is true'.

1. Statements: All mangoes are bananas (mango is a subset of banana); Some bananas are globe (a banana-globe overlap exists, but its exact position within banana is not fixed); All globe are square (globe is a subset of square).

2. Case A — draw the banana-globe overlap so that it includes the mango subset: every mango then falls inside globe, and since globe is a subset of square, every mango is square. This satisfies 'Some mangoes are square' (Conclusion I).

3. Case B — draw the banana-globe overlap so that it lies entirely outside the mango subset (no mango touches globe), and additionally draw the mango subset entirely outside the square region too — nothing in the statements forces mango and square to overlap. This diagram is still fully consistent with all three statements, and here no mango is square, satisfying 'No mango is square' (Conclusion II).

4. Both Case A and Case B are valid diagrams consistent with every statement, so neither conclusion follows definitely on its own.

Cross-check: 'Some mangoes are square' and 'No mango is square' are mutually exhaustive opposites — every possible diagram falls into one case or the other. Since each case is independently achievable, exactly one of the two conclusions must always hold, confirming that 'Either conclusion I or conclusion II is true' is the correct choice.