Questions: True and False Statements

Question 1

Which of the following is a statement?

• A. 'What time is it?' — a question about time
• B. 'Please sit down' — a polite instruction
• C. '7 is greater than 3' — a claim that is either true or false
• D. 'Hooray!' — an expression of excitement

Answer: (C)

A statement is a sentence that is either true or false. '7 is greater than 3' is a statement — it makes a claim that can be checked (and it happens to be true). A question asks for information, a command gives an instruction, and an exclamation expresses emotion. None of those are true or false, so none are statements in the logical sense.

Question 2

The sentence '2 + 2 = 5' is not a statement because it is wrong.

• T. True
• F. False

Answer: False

Being wrong does not disqualify a sentence from being a statement. '2 + 2 = 5' is a statement — it makes a definite claim that can be evaluated as true or false. It happens to be false. In logic, true statements and false statements are both statements. What matters is not whether the statement is correct, but whether it is the kind of sentence that CAN be true or false.

Question 3

An opinion like 'chocolate ice cream is the best flavor' is a true-or-false statement.

• T. True
• F. False

Answer: False

Opinions depend on personal preference and do not have a single definite truth value. 'Chocolate is the best flavor' is true for some people and false for others — logic requires that a statement be definitely one or the other, not a matter of perspective. Factual claims like 'chocolate ice cream contains cocoa' are statements because they can be verified.

Question 4

Why is it important in logic that every statement must be either true or false, with no middle ground?

Model answer: Because logical reasoning depends on being able to evaluate whether claims are true or false. If a statement could be 'sort of true' or 'maybe false,' you could not build reliable arguments from it. The true-or-false requirement — called the law of excluded middle — ensures that every logical operation (and, or, not, if-then) produces definite results. Without it, logical reasoning would have no solid foundation.

This principle is one of the three classical laws of logic (alongside the law of non-contradiction and the law of identity). While there are advanced logical systems that relax this requirement, classical logic — and the everyday reasoning students are learning — is built on the assumption that statements have definite truth values.