Three worked examples show how to test sweeping statements, avoid reversing a rule, and distinguish a possible cause from a proven one.
A review says a restaurant must be good because it is expensive. A colleague says everyone who works late is committed. A product advert promises that its method always works. Each statement moves from something we can observe to a conclusion that needs more support. You do not need a formal logic course to begin checking these claims. Ask whether the stated facts could be true while the conclusion is false. An expensive meal could be disappointing. Someone might work late because they were given too much to do. One genuine failure would contradict a promise that a method always works.
The examples below make these distinctions easier to see before applying them to messier arguments. They are practice questions with stated rules, so use the information provided rather than inventing a reason to disregard it. The useful skill is identifying exactly what the evidence allows you to conclude—and what it leaves open.
Every guide at the museum wears a green badge. Rina wears a green badge. Must Rina be a guide? Write yes or no, then give a reason. If you choose no, invent a situation where both facts are true but Rina is not a guide. Here is one answer: guides and gift-shop staff both wear green badges. Rina works in the gift shop. Every guide still has a green badge, and Rina has one too. Yet she is not a guide. The original rule goes one way. Being a guide is enough to tell you about the badge. Having the badge is not enough to tell you the job.
Now add this fact: only guides wear green badges. Rina wears one. Does the answer change? Yes. The new rule rules out the gift-shop example. The answer changes because the second version gives stronger information. The first rule permits other staff to wear green badges; the second reserves them for guides. Identifying that difference is the reasoning task. Try to state the difference in plain words. First version: guides have this badge, but other people might too. Second version: the badge is kept for guides alone.
The formal ideas behind this exercise are covered in OpenStax's section on logical arguments. You do not need its symbols to work through our examples.
A friend says that any number bigger than ten is even. What is the smallest whole number that breaks the claim? Eleven is the smallest whole number greater than ten, and it is odd. It therefore contradicts the claim that every number greater than ten is even. You only need one valid counterexample to disprove that universal statement. Now the friend changes the claim: some numbers bigger than ten are even. Does eleven break that version? No. Twelve is enough to show that some are even.
All and some do very different jobs. A case that defeats one claim may leave another untouched. Before looking for a flaw, make sure you know which claim is actually on the table.
If the sprinklers run, the garden path gets wet. You see a wet path. Does that prove the sprinklers ran? No. Rain could have wet the path. Someone could have washed it. In each case, something else made the path wet. This does not prove the sprinklers were off. It shows that the wet path alone cannot settle it. To learn what happened, you need more evidence, such as a timer record or someone who saw the sprinklers running. That distinction is easy to lose. Not proved does not mean false. It means the facts given leave more than one answer open.
A counterexample must follow the facts in the question. You cannot break the badge rule by saying a guide forgot the badge if the puzzle asks you to accept that every guide wears one. Keep the starting facts true. Then ask whether the conclusion could still be false. If it could, you have found a gap in the reasoning. This keeps the exercise fair. Otherwise, you could reject any argument by changing its rules. The useful skill is to find the weakness that is already there.
Write the case in one or two sentences. Long stories can hide a change to the facts. A short example is easier for someone else to check.
Suppose someone says a good student always gets high marks. You might think of a student who understands the work but misses a test through illness. The case challenges always. But do not use one example to pretend you have measured how often something happens. One case can break an absolute claim. It cannot by itself tell you the usual rate. For that, you need data. Logic and counting answer different questions. Can this happen? is not the same as How often does it happen? This is why I prefer precise claims. Students who study often do better leaves room for variation. Every good student gets high marks does not.
Apply the same check to a claim you encounter this week. Write down the claim, the evidence offered for it, and an alternative explanation that fits that evidence. If the statement uses “all,” “always,” or “never,” consider what kind of real example would contradict it. Be equally careful with your objection. One exception can disprove a universal claim, but it cannot tell you how common the exception is. A possible alternative explanation can show that a conclusion is not yet established, but it does not prove your alternative happened. That distinction makes the exercise useful for understanding an argument rather than merely winning one.
