Q.Which of the following sentences are statements? Give reasons for your answer.

1. "There are 35 days in a month." Has a definite truth value — it is false (no month has 35 days). Statement.
2. "Mathematics is difficult." A matter of personal opinion, varies by person. Not a statement.
3. "The sum of 5 and 7 is greater than 10." $5+7=12>10$ — definitely true. Statement.
4. "The square of a number is an even number." Ambiguous — true for some numbers (e.g., 4² = 16), false for others (e.g., 3² = 9); no fixed truth value since "a number" is unspecified. Not a statement.
5. "The sides of a quadrilateral have equal length." True for some quadrilaterals (e.g., square) and false for others (e.g., rectangle); ambiguous. Not a statement.
6. "Answer this question." This is a command/imperative, not declarative. Not a statement.
7. "The product of (–1) and 8 is 8." $(-1)\times 8 = -8 \ne 8$ — definitely false. Statement.
8. "The sum of all interior angles of a triangle is 180°." A fixed geometric fact — true. Statement.
9. "Today is a windy day." Depends on the place and day it is uttered — no fixed, context-free truth value. Not a statement.
10. "All real numbers are complex numbers." Every real number a can be written as a + 0i, a complex number — true. Statement.
    ✓Final answer

    Statements: (i), (iii), (vii), (viii), (x). Not statements: (ii), (iv), (v), (vi), (ix).

For each sentence, check: is it declarative? Does it have one fixed truth value independent of the speaker, time, or unspecified variables? Reject sentences that are opinions, ambiguous/variable-dependent, or non-declarative (questions/commands).

• Treating a sentence with an unspecified variable ("a number", "a quadrilateral") as a statement even though its truth varies by which value is substituted.
• Missing that "today is windy" is context-dependent (different truth on different days/places), so it is not a statement even though it sounds factual.