KBAT Problems
KBAT Problem: Testing an Argument
A KBAT problem where you must judge whether a conclusion really follows from given statements, logic, not calculation.
Separate premises from conclusion
You are given two statements and a claimed conclusion. First write each as a clear logical statement, then check whether the conclusion is forced by the premises or only looks plausible.
A counter-example is enough to show an argument is not valid.
Understand the problem
Judge whether this argument is valid. Premise 1: If a number is a multiple of 6, then it is a multiple of 3.
Premise 2: 18 is a multiple of 6. Conclusion: Therefore 18 is a multiple of 3.
What it really asks: decide whether the conclusion is forced by the premises, not whether it merely happens to be true, that difference is the whole point of logical reasoning.
Plan and solve
- Write each statement in the form 'If p then q'. Let p be 'a number is a multiple of 6' and q be 'it is a multiple of 3'.
- Premise 1 is 'If p then q'. Premise 2 states p is true for 18. The conclusion states q is true for 18.
- This matches the valid Argument Form 'If p then q; p is true; therefore q is true'. The pattern itself makes the conclusion certain.
- So the argument is valid, the conclusion follows necessarily from the premises.
Check and a variant
Check the reasoning is about form, not luck: any p and q in that pattern give a valid argument. A variant the examiner could add keeps Premise 1 but changes Premise 2: '9 is a multiple of 3; therefore 9 is a multiple of 6.'
This is not valid, it assumes q to prove p, and the counter-example 9 (a multiple of 3 but not of 6) breaks it. One counter-example is enough to show an argument fails.
Frequently asked questions
What is the difference between a statement being true and an argument being valid?
Truth is about a single statement matching the facts; validity is about whether a conclusion is forced by its premises. An argument can reach a true conclusion by a faulty route, and that is still not valid.
In logic questions you are graded on the reasoning pattern, not just on whether the ending line is correct.
How does a counter-example prove an argument is not valid?
A counter-example is a single case where the premises are all true but the conclusion is false. If even one such case exists, the premises do not force the conclusion, so the argument is not valid.
Finding one clear counter-example is a complete and marker-friendly way to disprove an argument.
Do I need to memorise the named argument forms for SPM?
Know the standard valid forms well enough to recognise and name them, because the exam often asks you to identify one. More important is understanding why each form works, so you can spot when an argument only looks like a valid form but actually swaps the premises.
Recognition plus reasoning is what earns full marks.