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Simple Statements

A free Logic lesson from the “Statements and Negation” unit, with a worked example and practice problems including step-by-step solutions.

Simple statements make one claim. They are the atoms of logic: before combining statements, students need to know what the basic claim is. Learning objective: Recognize a single logical claim. Prerequisite: No formal prerequisite. Work in this lesson starts with ordinary language, then connects the idea to symbols only after the meaning is clear. Example 1: '7 is prime' is a statement because it can be true or false. Example 2: 'Is 7 prime?' is not a statement because it asks a question instead of making a claim. A common misconception is to treat familiar wording as proof; instead, check exactly what the statement says and what follows from it.

What you'll learn

Why it matters: Statements and non-statements appear in instructions, word problems, proofs, and computer conditions.

Worked example

Problem. Example case A (Simple Statements): Worked example: Which rule or habit best matches Simple Statements?

  1. Simple Statements targets a specific reasoning habit.
  2. Simple Statements focuses on recognize a single logical claim.
  3. The other choices either overclaim or change the logical relationship.

Answer: Simple Statements focuses on recognize a single logical claim.

Practice problems

1. Practice case A (Simple Statements): Is "Every square has four equal sides." a logical statement?

Choices: Yes, it makes a claim. · No, it is only a command. · No, it is only a question. · No, statements cannot use numbers.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Practice case A (Simple Statements): Is "Every square has four equal sides." a logical statement?
  2. Compare each choice with the stated logical rule, and eliminate choices that change the claim's meaning.
  3. It makes a mathematical claim.
  4. A logical statement needs a possible truth value.
  5. This sentence qualifies.
  6. Verify the selected choice by checking that it preserves the stated logical meaning and that the other choices change the rule or claim.

Answer: Yes, it makes a claim.

2. Practice case B (Simple Statements): Which is a compound statement?

Choices: x is positive and x is even. · x is positive. · What is x? · Solve for x.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Practice case B (Simple Statements): Which is a compound statement?
  2. Compare each choice with the stated logical rule, and eliminate choices that change the claim's meaning.
  3. A compound statement joins simpler claims.
  4. The word and connects two claims.
  5. So the first choice is compound.
  6. Verify the selected choice by checking that it preserves the stated logical meaning and that the other choices change the rule or claim.

Answer: x is positive and x is even.

3. Practice case C (Simple Statements): If p means "the number is even," write the symbolic form of "not p."

Show solution
  1. Warm-up: First identify exactly what the question is asking: Practice case C (Simple Statements): If p means "the number is even," write the symbolic form of "not p."
  2. Read the statement in plain English first, then match the symbol, connective, quantifier, or argument form to that meaning.
  3. The symbol ¬ means not.
  4. Place ¬ before the statement letter.
  5. The symbolic form is ¬p.
  6. Check the response against the original logical form: it should match ¬p without changing the meaning.

Answer: ¬p

4. Practice case D (Simple Statements): Which sentence has an unknown truth value because the variable has not been specified?

Choices: x is greater than 10. · 10 is greater than 5. · Close the book. · What is 10?

Show solution
  1. Warm-up: First identify exactly what the question is asking: Practice case D (Simple Statements): Which sentence has an unknown truth value because the variable has not been specified?
  2. Compare each choice with the stated logical rule, and eliminate choices that change the claim's meaning.
  3. The sentence with x makes a claim.
  4. Its truth depends on the value of x.
  5. So it is unknown until x is specified.
  6. Verify the selected choice by checking that it preserves the stated logical meaning and that the other choices change the rule or claim.

Answer: x is greater than 10.

5. Practice case E (Simple Statements): Lesson focus: Which transfer task would show readiness for Simple Statements?

Choices: Apply recognize a single logical claim in a new sentence or context. · Repeat the exact worked example without changing the context. · Pick an answer before identifying the claim parts. · Use a rule from another lesson because the words sound close.

Show solution
  1. A transfer task keeps the same objective but changes the surface context.
  2. Apply recognize a single logical claim in a new sentence or context.
  3. That is a better mastery signal than memorizing a practice prompt.

Answer: Apply recognize a single logical claim in a new sentence or context.

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