Q.Which of the following sentences are statements in logic? Justify. Write down the truth value of the statement: $\cos^2\theta - \sin^2\theta = \cos 2\theta$ for all $\theta \in \mathbb{R}$.

A statement in mathematical logic is a declarative (assertive) sentence that has exactly one truth value: it is either true (denoted T) or false (denoted F), never both at once and never undetermined. Statements are named using lowercase letters such as p, q, r for convenience. Sentences that ask a question, give a command or request, express an exclamation, or whose truth genuinely depends on who is speaking, when, or on an unassigned variable (for example 'x + 6 = 9', 'he is tall', or 'it is black in colour') are called open sentences and are NOT statements in logic, because no single fixed truth value can be pinned to them. Reco …