Arguments: Premises and Conclusions
A free Logic lesson from the “Foundations of Logical Thinking” unit, with a worked example and practice problems including step-by-step solutions.
A premise supplies a reason; a conclusion is the claim those reasons are meant to establish. Identify roles from the reasoning, not just sentence order. To check an inference, assume its premises and ask whether the conclusion could still be false.
What you'll learn
- Identify premises and conclusions in a short argument
- Explain the idea in plain English before using symbols
- Use examples, non-examples, or counterexamples to check the reasoning
Worked example
Problem. Every archive member has a pass. Mira is a archive member. Therefore Mira has a pass. Identify the conclusion.
- The first two claims are reasons.
- The therefore-clause is the claim those reasons support.
Answer: Mira has a pass
Lesson preview: this page shows 5 practice items. The interactive activity contains 6 practice items and 6 quiz items (multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Every archive member has a pass. Mira is a archive member. Therefore Mira has a pass. Identify the conclusion.
Choices: Mira is a archive member · Every pass holder is a member · Mira has a pass · Every archive member has a pass
Show solution
- The first two claims are reasons.
- The therefore-clause is the claim those reasons support.
Answer: Mira has a pass
2. Every multiple of 38 is even. 114 is a multiple of 38. Which conclusion follows?
Choices: Every even number is a multiple of the given number · 114 is even · Every even number equals 114 · 38 is odd
Show solution
- Apply the universal premise to the specific multiple.
Answer: 114 is even
3. All bronze tokens open the gate. This token opens the gate. Does it follow that the token is bronze?
Choices: No; a token of another material may also open it · Yes, by modus ponens · Yes, because the conclusion is repeated · No; it must be silver
Show solution
- The premise gives one sufficient condition, not the only possible condition.
Answer: No; a token of another material may also open it
4. All members are registered. Ada is a member. Which premise is needed to conclude Ada is registered?
Choices: All registered people are members · No members are registered · Ada is registered · All members are registered
Show solution
- The universal premise connects membership to registration.
- Do not assume the desired conclusion as the missing reason.
Answer: All members are registered
5. The conclusion appears first: “The switch is off, because an on switch lights the lamp and the lamp is not lit.” Which claim is the conclusion?
Choices: The lamp is not lit · The lamp is broken · The switch is off · An on switch lights the lamp
Show solution
- Sentence order does not determine argumentative role.
- Because introduces the supporting premises.
Answer: The switch is off
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