True and False Statements

Learn to identify and evaluate statements as true or false.

Elementary15 minLesson
Printable worksheet

Definition

A statement is a sentence that is either true or false, but not both.
In mathematics and logic, we work with statements that can be clearly evaluated:
True statements are correct. They match reality or follow mathematical rules:
  • "" is true
  • "A square has 4 sides" is true
False statements are incorrect. They do not match reality:
  • "" is false
  • "A triangle has 5 sides" is false
Not every sentence is a statement! Questions ("What is ?") and commands ("Add these numbers") are NOT statements because they cannot be true or false.

Try it now

Which of these is a TRUE statement?

Worked Examples

Is the statement "" true or false?

1

Identify the statement

The statement claims that 8 plus 5 equals 13 →

2

Calculate the left side

→ 13

3

Compare with the right side

Left side: 13, Right side: 13 → 13 = 13

4

Determine if true or false

Both sides are equal → TRUE

Common Mistakes

Thinking questions can be true or false

Why it's wrong: "What is 5 + 3?" is a question, not a statement. It asks for information rather than making a claim.

Correct: Only declarative sentences that make a claim can be true or false. "5 + 3 = 8" is a statement.

Confusing "sometimes true" with true statements

Why it's wrong: "It is raining" is sometimes true and sometimes false depending on the weather.

Correct: In math logic, a true statement is ALWAYS true. "" is always true, not just sometimes.

Thinking false means "bad" or "wrong to say"

Why it's wrong: False simply means the statement does not match reality. It is not a judgment about the person.

Correct: False is a logical classification. "" is false because 3 is not greater than 5.

Interactive Sandbox

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Practice Problems

15 problems
Problem 1 of 15
Easy

Which of these is a TRUE statement?

Why It Matters

Understanding true and false statements is the foundation of logical thinking:
  • Problem Solving: When you check your math work, you evaluate whether your answer makes the statement true
  • Science: Scientists test hypotheses to determine if they are true or false
  • Computer Programming: Computers use true/false logic to make decisions
  • Daily Life: You constantly evaluate claims - "The store closes at 9 PM" is either true or false
Learning to identify and evaluate statements helps you think critically and make better decisions!

Real World Applications

Fact-Checking Information

When you read news or information online, you evaluate whether statements are true or false.

Example:

If someone says "The Earth is the largest planet in our solar system," you can check: Is this true or false? (It is false - Jupiter is the largest.)

Testing Answers in Math

When you solve a math problem, you can check your answer by substituting it back.

Example:

If you solve and get , check: Is "" true? Yes! Your answer is correct.

Computer Programs

Computers use true/false logic constantly to make decisions.

Example:

A game checks: "Is the player's score greater than the high score?" If TRUE, save new high score. If FALSE, keep the old one.

Key Takeaways

  • 1A statement is a sentence that is either true or false, but not both
  • 2True statements are correct and match mathematical rules or reality
  • 3False statements are incorrect and do not match reality
  • 4Questions and commands are NOT statements
  • 5In math, true statements are ALWAYS true, not just sometimes

Frequently Asked Questions

No! In logic, every statement must be exactly one: either true OR false. This is called the Law of the Excluded Middle.
No! In logic, every statement must be exactly one: either true OR false. This is called the Law of the Excluded Middle.
This is tricky! It is a statement (it can be true or false), but its truth depends on the person saying it. In math, we prefer statements with clear, objective truth values like "".
Even if we do not know whether something is true, it still has a truth value. "There are exactly 100 grains of sand on this beach" is either true or false - we just might not know which.

Glossary

Statement
A sentence that is either true or false, but not both
True
A statement that correctly describes reality or follows mathematical rules
False
A statement that does not correctly describe reality
Evaluate
To determine whether a statement is true or false
Counterexample
An example that proves a statement is false

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