Logical Reasoning · 3.2.6
Solving problems in logical reasoning
This standard requires students to apply everything learned in the logical reasoning topic, statements, negation, compound statements, implications and arguments, together to solve real or mathematical problems, choosing the correct reasoning tools and combining them to reach and justify a sound conclusion.
The official learning standard (3.2.6)
“Solve problems involving logical reasoning.”
What it means
This standard requires students to apply everything learned in the logical reasoning topic, statements, negation, compound statements, implications and arguments, together to solve real or mathematical problems, choosing the correct reasoning tools and combining them to reach and justify a sound conclusion.
How it is examined
This standard is examined mainly in Paper 2 as multi-step structured questions combining statements, implications and arguments within one real-life or mathematical scenario. It may also appear in Paper 1 as objective items testing overall understanding across several logical reasoning subtopics.
Worked example
Given the implication: 'If a number is divisible by 6, then it is divisible by 3.' (a) Write the converse of this implication.
(b) State whether the converse is true, giving a counter-example if it is false.
- Original implication: p is 'a number is divisible by 6', q is 'a number is divisible by 3'. Form: if p then q.
- Converse: if q then p, that is, 'if a number is divisible by 3, then it is divisible by 6.'
- Test the converse with an example: take the number 9. 9 is divisible by 3 (q is true) but 9 is not divisible by 6 (p is false).
- Since a case is found where q is true but p is false, the converse is false.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What kind of problems combine several logical reasoning subtopics in one question?
Typical exam problems give a statement or implication in a real or mathematical context, then ask students to negate it, form its converse, inverse or contrapositive, determine truth values, and sometimes build a related argument, all within the same scenario, testing several skills together.
How should I approach a word problem asking me to justify a conclusion using logical reasoning?
First identify the given statements clearly, labelling them p, q and so on if useful. Decide whether the reasoning is deductive or inductive, apply the correct rule or pattern, then write your justification in full sentences linking the premises directly to the conclusion.
Are Venn diagrams or truth tables required for these logical reasoning problems?
They are not always required but are very useful tools. A truth table can systematically check compound statements or implications, while listing cases clearly helps organise reasoning about arguments; use whichever method makes your working clear and easy for an examiner to follow.