Q.Which of the following sentences are statements in logic? Justify. Write down the truth value of the statement: If $x$ is a whole number then $x + 6 = 0$.

"If $x$ is a whole number then $x+6=0$" contains the variable $x$ with no quantifier (no "for all $x$" or "there exists $x$") attached to it. Its truth value genuinely depends on which value $x$ takes: if $x$ is not a whole number the conditional is vacuously True (false antecedent), while if $x$ IS a whole number the conditional is False (since $x+6=0$ never holds for $x \ge 0$). Because the truth value is not fixed without specifying $x$, this is an open sentence (a …

Check whether every variable is bound by a quantifier or a fixed value; an unbound variable makes the …

Assuming any sentence with an 'if...then' structure is automatically a statement, without checking w …