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:
  • "2+3=52 + 3 = 5" is true
  • "A square has 4 sides" is true
False statements are incorrect. They do not match reality:
  • "2+3=72 + 3 = 7" is false
  • "A triangle has 5 sides" is false
Not every sentence is a statement! Questions ("What is 2+32 + 3?") 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 "8+5=138 + 5 = 13" true or false?
1

Identify the statement

The statement claims that 8 plus 5 equals 13 → 8+5=138 + 5 = 13
2

Calculate the left side

8+5=138 + 5 = 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. "2+2=42 + 2 = 4" 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. "3>53 > 5" 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 x+5=12x + 5 = 12 and get x=7x = 7, check: Is "7+5=127 + 5 = 12" 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 "5>35 > 3".
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
Today's challengeOne problem, three tries

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