Logical Reasoning
Implication
A statement of the form "if p, then q", linking a condition to a conclusion.
| English | Implication |
|---|---|
| Bahasa Melayu | Implikasi |
| 中文 | 蕴含 |
How it is used
"If a number is a multiple of 10, then it is a multiple of 5" is an implication of the form "if p, then q". Here p is "the number is a multiple of 10" (the antecedent) and q is "it is a multiple of 5" (the consequent); this implication is true.
Where it shows up in SPM
Implication is a core Form 4 topic. Paper 1 asks you to identify the antecedent and consequent or to complete "if ..., then ...".
Paper 2 often asks you to write two implications from a statement using "if and only if", and to state a converse.
Don't confuse it with
Open the chapter: Logical Reasoning →
Frequently asked questions
What are the antecedent and consequent?
In "if p, then q", the antecedent is p (the condition after "if") and the consequent is q (the result after "then"). In "if x = 3, then x² = 9", the antecedent is "x = 3" and the consequent is "x² = 9".
How do I split "p if and only if q" into implications?
Write two implications: "if p, then q" and "if q, then p". For "a triangle is equilateral if and only if its three sides are equal", you get "if a triangle is equilateral, then its three sides are equal" and its reverse.
Is an implication still true if the antecedent is false?
In SPM you mainly judge implications from their meaning rather than a full truth table. Focus on whether the consequent must follow when the antecedent holds; if you can find a case where p is true but q is false, the implication fails.