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.
An argument gives reasons for a claim. The premises are the support, and the conclusion is the claim those reasons are meant to prove or justify. Learning objective: Identify premises and conclusions in a short argument. 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: 'All squares are rectangles' is a claim; 'Draw a square' is a command. Example 2: In 'All squares are rectangles, and this is a square, so this is a rectangle,' the first two sentences are premises and the last sentence is the conclusion. 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
- 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. Example case A (Arguments: Premises and Conclusions): Worked example: Which rule or habit best matches Arguments: Premises and Conclusions?
- Arguments: Premises and Conclusions targets a specific reasoning habit.
- Premises give the reasons; the conclusion is the claim those reasons support.
- The other choices either overclaim or change the logical relationship.
Answer: Premises give the reasons; the conclusion is the claim those reasons support.
Practice problems
1. Practice case A (Arguments: Premises and Conclusions): Classify the sentence "The number 18 is divisible by 3."
Choices: Statement · Question · Command · Fragment
Show solution
- It makes a claim that can be checked.
- Logic starts by deciding whether a sentence makes a true-or-false claim.
- The best classification is Statement.
Answer: Statement
2. Practice case B (Arguments: Premises and Conclusions): In the argument "All multiples of 6 are even. 24 is a multiple of 6. Therefore, 24 is even," which sentence is the conclusion?
Choices: 24 is even. · All multiples of 6 are even. · 24 is a multiple of 6. · 6 is even.
Show solution
- The conclusion is what the premises support.
- The word therefore signals the conclusion.
- So the conclusion is 24 is even.
Answer: 24 is even.
3. Practice case C (Arguments: Premises and Conclusions): Which wording is most precise for a math claim?
Choices: Every integer greater than 2 is positive. · Numbers are usually big. · It works most of the time. · That answer feels right.
Show solution
- Precise claims say exactly which objects are included.
- Every integer greater than 2 is positive can be checked.
- The other choices use vague language.
Answer: Every integer greater than 2 is positive.
4. Practice case D (Arguments: Premises and Conclusions): A valid argument is best described as one where:
Choices: the conclusion must follow if the premises are true · the premises are always short · the conclusion is probably popular · the words sound mathematical
Show solution
- Validity is about structure.
- Assume the premises are true and ask whether the conclusion is forced.
- That is the definition of validity.
Answer: the conclusion must follow if the premises are true
5. Practice case E (Arguments: Premises and Conclusions): Lesson focus: Which transfer task would show readiness for Arguments: Premises and Conclusions?
Choices: Identify the conclusion in a short argument with new wording. · 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
- A transfer task keeps the same objective but changes the surface context.
- Identify the conclusion in a short argument with new wording.
- That is a better mastery signal than memorizing a practice prompt.
Answer: Identify the conclusion in a short argument with new wording.
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