True and False Statements

Core Idea

A statement is a sentence that is either true or false — not both, and not neither. "Dogs have four legs" is a true statement. "The sun is cold" is a false statement. "Is it raining?" is not a statement (it is a question). "Wow!" is not a statement (it is an exclamation). Learning to distinguish statements from non-statements, and true statements from false ones, is the first step in logical thinking. Logic is built entirely on the idea that statements have definite truth values.

How It's Best Learned

Give students a mix of sentences and ask them to sort into three piles: "true statement," "false statement," and "not a statement." Include questions, commands, exclamations, opinions, and clearly true/false factual claims. Discuss borderline cases: is "chocolate is the best flavor" a statement? (It is an opinion, not a factual claim with a definite truth value — introduce this subtlety gently.) Use everyday examples to make the concept tangible.

Common Misconceptions

• Thinking a false statement is not a statement — false statements are still statements; they just happen to be false.
• Confusing statements with questions or commands — "Close the door" is a command, not something that can be true or false.
• Believing that statements must be true to count — the sentence "2 + 2 = 5" is a perfectly valid statement; it is just a false one.
• Thinking opinions are statements — "pizza is the best food" is subjective and does not have a definite truth value in logic.

Explainer

Before you can reason logically, you need to know what logic works with. The answer is statements — sentences that are either true or false. Not questions, not commands, not exclamations. Statements.

"The Earth orbits the Sun" is a statement — it is true. "Fish can fly" is a statement — it is false. "What is your name?" is NOT a statement — it is a question, and questions are neither true nor false. "Sit down, please" is NOT a statement — it is a command. "Wow, that is amazing!" is NOT a statement — it is an exclamation. The key test is: can you say whether this sentence is true or false? If yes, it is a statement. If no, it is not.

Here is something that surprises many students: false statements are still statements. The sentence "2 + 2 = 5" is wrong, but it is still a statement. It makes a clear claim that can be checked. It just happens to fail the check. In logic, being false is not a disqualification — it is a classification. Every statement has a truth value: true or false. That truth value is what logic operates on.

One tricky case: opinions. Is "pizza is the best food" a statement? In everyday conversation, people say "that is true!" But in logic, this sentence does not have a definite truth value — it depends on who you ask. Logic works with claims that can be objectively evaluated, like "pizza contains cheese" (true, usually) or "pizza was invented in the year 1000" (can be checked). Separating factual claims from opinions is part of learning to think logically.

This idea — that statements are true or false, and everything in logic starts from there — is the foundation of all the logical reasoning you will learn next. When you study "if-then" statements, "and" and "or," and negation, every one of those operations takes statements as input and produces statements as output. Getting clear on what a statement is will make everything else easier.