<p>Which of the following is not a proposition?</p>
<p>\(\sqrt{3}\) is a prime</p>
<p>\(\sqrt{2}\) is irrational</p>
<p>Mathematics is interesting</p>
<p>5 is an even integer</p>
Step-by-Step Solution
Key Concept: A proposition is a declarative statement that is either definitely true or definitely false—never both, never neither, and never indeterminate. Exclamations, questions, commands, and statements with free variables are not propositions.
<p><strong>Step 1:</strong> Recall the definition of a proposition: A proposition is a declarative sentence that has a definite truth value (either true or false, but not both or neither).</p><p><strong>Step 2:</strong> Identify what is NOT a proposition:</p><ul><li>Exclamations (e.g., 'What a beautiful day!') — express emotion, not a claim</li><li>Questions (e.g., 'Is it raining?') — ask for information, not declarative</li><li>Commands/Imperatives (e.g., 'Close the door') — orders, not declarative statements</li><li>Open statements with free variables (e.g., 'x + 2 = 5') — truth value depends on x</li></ul><p><strong>Step 3:</strong> Among the given options, select the one that is an exclamation, question, command, or open statement without quantifiers.</p><p>∴ Answer: C</p>
Correct Answer: C