Logical Reasoning · Form 4
Logical Reasoning: Revision Notes
A tight revision summary of Logical Reasoning for SPM Mathematics, the key ideas, the formulae the exam gives you, and what to focus on before the paper.
The big idea
This chapter treats sentences as mathematical objects. You learn what makes a statement true or false, how to negate it, how to combine statements with “and”, “or” and “if… then”, and how to tell whether an argument is valid.
It is precise, careful work rather than heavy computation.
Key ideas to revise
- Statements have a truth value. A statement is a sentence that is either true or false, a question or command is not a statement.
- Negation, “and”, “or”. Negating flips the truth value; “and” is true only when both parts are; “or” is true when at least one is.
- Implication and argument forms. From “if p then q” you learn to build valid arguments and spot invalid ones, the heart of the chapter.
Every key idea walked through in one line
- Truth value: 'A triangle has 3 sides' is a statement and is true; 'Draw a triangle' is a command, so it carries no truth value and can never enter a truth table, only the first sentence can.
- Negation, 'and', 'or': let p: '6 > 4' (true) and q: '6 is odd' (false). Then ~p: '6 ≤ 4' is false; 'p and q' = true and false = false; 'p or q' = true or false = true.
- Implication and argument: from 'If n = 4 then n² = 16', add the premise 'n = 4'; the valid conclusion is 'n² = 16' the modus ponens form p → q, p, therefore q.
A pre-paper checklist for the logic questions
- Re-derive the four truth-table templates from scratch: ~p flips p; p ∧ q is true only when both are true; p ∨ q is true when at least one is true; p → q is false only when p is true and q is false.
- Know what the exam hands you: the statements themselves, and often a half-filled truth table or an argument missing its conclusion. You supply truth values, a negation, or a conclusion, never a new formula, because logic has none to memorise.
- Count your rows before filling them: n simple statements need 2ⁿ rows, 2 statements give 4 rows, 3 statements give 8 rows. A missing row is a lost completeness mark.
- The one habit that saves marks: write every truth table in full, and for any validity question add a sentence of reason 'valid, modus ponens' or a specific counter-example, never the bare word 'valid'.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Can I just reason the answer out in my head instead of drawing the truth table?
You can, but you should not in Paper 2. The completed rows are themselves worth working marks, so a table shown in full protects you even if your final value slips.
Reasoning silently risks losing the whole part to one careless flip, with nothing on paper for the marker to credit.
How many rows does my truth table need?
Count the number of distinct simple statements, call it n, and the table needs 2ⁿ rows. One statement needs 2 rows, two statements need 4, three need 8.
List them in a fixed order (TT, TF, FT, FF for two) so you never repeat or skip a combination, a missing row costs the completeness mark.
What is the fastest way to revise this chapter the night before?
Redraw the four templates ~p, p ∧ q, p ∨ q, p → q from blank paper, then practise three moves: decide if a sentence is a statement, negate one compound statement, and judge one argument with a reason. Those three cover almost every mark the chapter offers, and none needs a memorised formula.