The symbol ∇ represents one of the following operations: addition,…

Concept: In a data-sufficiency question, a given statement is sufficient only if it narrows the unknown to exactly one outcome. Test each candidate value/operation against the statement — if more than one candidate survives the test, the statement leaves the answer ambiguous and is not sufficient.

1. Apply statement (1), 0 ∇ 1 = 1, to each of the four candidate operations: 0+1=1 (matches), 0-1=-1 (no), 0×1=0 (no), 0÷1=0 (no).

2. Only addition survives, so ∇ is uniquely determined to be addition, and 3 ∇ 2 = 3+2 = 5. Statement (1) alone is sufficient.

3. Apply statement (2), 1 ∇ 0 = 1, to each of the four candidate operations: 1+0=1 (matches), 1-0=1 (matches), 1×0=0 (no), 1÷0 is undefined (no).

4. Two operations survive — addition and subtraction — so ∇ is not pinned down: 3 ∇ 2 could be 3+2=5 or 3-2=1. Statement (2) alone is not sufficient.

Cross-check: the operation fixed by statement (1) (addition) also satisfies statement (2)'s equation (1+0=1), so the two statements are consistent with each other; statement (2) is simply loose enough to also admit subtraction, which is exactly why it cannot stand alone.

Result: statement (1) alone fixes a single value for 3 ∇ 2, while statement (2) alone permits two different values, so statement (1) ALONE is sufficient but statement (2) alone is not.