Logical Reasoning · Form 4
Logical Reasoning: Paper 2 Answering Guide
How Logical Reasoning appears in Mathematics Paper 2 (Subjective), and how to lay out your working so you earn every method mark.
How it is examined
Questions are wordy and reward students who read slowly. Paper 2 often asks you to complete a truth table, negate a compound statement, or judge an argument’s validity with a reason.
The maths is light; the marks are in precision and clear justification.
Showing your working
Mathematics Paper 2 (Subjective) is worth 100 marks and gives marks for the steps, not only the answer. Write each line clearly: state the formula or rule, substitute the numbers, then simplify.
If the question carries units, carry them through to the final line.
A worked Paper-2 logic question, mark by mark
Paper 2 style. Given the statements p: '18 is a multiple of 6' and q: '18 is a multiple of 4'.
(a) State the truth value of p and of q. (b) Write the compound statement 'p and q' in words and state its truth value.
(c) Construct a truth table for 'p or q'. (d) Consider the argument, 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. Write the conclusion, and state with a reason whether the argument is valid.
- (a) p: 18 = 6 × 3, so p is true. q: 18 ÷ 4 = 4.5, not a whole number, so q is false.
- (b) 'p and q': '18 is a multiple of 6 and 18 is a multiple of 4.' Rule: a conjunction is true only when both parts are true. Here true and false, so 'p and q' is false.
- (c) 'p or q' is a disjunction, false only when both are false. List all 2² = 4 rows: p = T, q = T → T; p = T, q = F → T; p = F, q = T → T; p = F, q = F → F.
- (d) Rule (modus ponens): from p → q and p, conclude q. Conclusion: '18 is a multiple of 3.' The argument is valid, because the conclusion follows from the two premises by the form p → q, p, ∴ q (deductive reasoning).
The same question, three ways examiners re-dress it
The layout above transfers to the common re-dressings. If the argument were re-worded as 'Premise 2: 20 is a multiple of 6', the conclusion still reads by modus ponens, but you must state the argument is not sound because the premise is false while the form stays valid, keep validity (form) and soundness (true premises) separate.
If part (c) instead asked for p → q, remember its column is T, F, T, T down the four rows. And if the negation of a quantifier is asked, 'All multiples of 6 are even' negates to 'At least one multiple of 6 is not even', never 'No multiple of 6 is even'.
Same four-move discipline, rule, substitute, simplify, answer, earns the marks whichever dressing appears.
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
In a validity question, do I get the mark for just writing 'valid'?
Usually not. Most schemes split the marks: one for the correct judgement and one for the reason.
So write 'valid' and then justify it, name the form such as modus ponens, or state that the conclusion follows from the premises. For an invalid argument, give a counter-example that fits the premises but breaks the conclusion.
Which order should I present the parts of a logic question?
Follow the labels (a), (b), (c) exactly and keep each part separate, examiners mark part by part. Within a part, put the rule or definition first, then your substitution, then the answer.
Never merge two parts into one block of working; if a later part depends on an earlier value, quote that value again rather than making the marker hunt for it.
How much working does a truth-table part actually need?
The full grid is the working. Draw all 2ⁿ rows with a column for each input and a final column for the compound statement, and fill every cell.
You do not need prose explanation, but every row must appear. A correct final column with missing rows still loses the completeness mark, so never abbreviate the table.