Logical Reasoning · Form 4
Logical Reasoning: Common Mistakes
The mistakes that quietly cost marks in Logical Reasoning, and how to avoid each one in the SPM exam.
In our experience teaching Logical Reasoning, most lost marks come from a small set of repeated slips, not from a lack of understanding. Here they are, with the fix for each.
Mistakes to avoid
- Negating only part of a compound statement
- Confusing an implication with its converse
- Calling a question or opinion a “statement”
Six more logic slips that quietly cost marks
- What students write: the negation of 'x > 5' is 'x < 5'. → Why it loses marks: it drops the boundary value x = 5, which the original excludes but the negation must include. → Correct working: ~(x > 5) is 'x ≤ 5'.
- What students write: mark 'p or q' as false when both p and q are true. → Why it loses marks: in mathematics 'or' is inclusive, so it is true when at least one part is true, both true still gives true. → Correct working: T ∨ T = true.
- What students write: mark the implication p → q as false whenever p is false. → Why it loses marks: p → q is false in the single case p true and q false; a false p makes the whole implication true. → Correct working: F → T = true and F → F = true.
- What students write: negate 'All students passed' as 'No students passed'. → Why it loses marks: the true negation needs only one exception, not the opposite extreme. → Correct working: 'At least one student did not pass' (some … not).
- What students write: a truth table with 2 rows for two statements p and q. → Why it loses marks: two statements have 2² = 4 combinations, so two rows leave half the cases untested. → Correct working: list all 4 rows, TT, TF, FT, FF.
- What students write: call an argument valid because its conclusion is a true fact. → Why it loses marks: validity depends on the form, does the conclusion follow from the premises? not on whether the conclusion happens to be true. → Correct working: check the form; p → q, p, ∴ q is valid, while a true conclusion drawn from a broken form is still invalid.
One self-check before you move on
Before leaving any logic answer, run three quick tests. First, re-read every 'or' as inclusive and every 'if…then' with only the p-true-q-false case as false.
Second, count that your truth table has exactly 2ⁿ rows for n statements. Third, for a negation of a quantifier check you wrote 'some…not' or 'at least one', not the opposite extreme, and that any inequality kept its boundary.
These three passes catch the six slips above in well under a minute.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Is 'or' in mathematics the same as the everyday 'either… or'?
No. Everyday speech often means exclusive or, one but not both, as in 'tea or coffee'.
Mathematics uses inclusive or: 'p or q' is true when p is true, when q is true, and when both are true. It is false only when both parts are false.
Judge every disjunction by that rule.
If the premises of an argument are false, can the argument still be valid?
Yes. Validity is about form, not truth.
If the conclusion must follow from the premises whenever they are assumed true, the argument is valid, even if those premises happen to be false in reality. So never reject an argument as invalid just because a premise looks untrue; test whether the conclusion follows.
Why is 'if p then q' true when p is false?
Because an implication only promises something about the case where p happens. If p never happens, the promise is never broken, so it counts as true.
Think of 'If it rains, I bring an umbrella': on a dry day you have broken no promise. The only way to make p → q false is p true with q false.