Logical Reasoning · 3.1.2
Negating a statement
Students learn to form the negation of a given statement by inserting 'not' or 'no' at the correct point in the sentence, producing a new statement with the opposite meaning. The negation must always have the opposite truth value from the original statement, if one is true, the other must be false.
The official learning standard (3.1.2)
“Negate a statement by changing its truth value through inserting the word 'not' or 'no'.”
What it means
Students learn to form the negation of a given statement by inserting 'not' or 'no' at the correct point in the sentence, producing a new statement with the opposite meaning. The negation must always have the opposite truth value from the original statement, if one is true, the other must be false.
How it is examined
This is tested in Paper 1 as short objective items, where students write the negation of a given statement, or are given a statement and its negation and must state the truth value of each. It may also appear combined with truth-table style reasoning questions.
Worked example
Write the negation of the statement '12 is an even number' and state its truth value.
- Identify the original statement: '12 is an even number', which is true since 12 can be divided exactly by 2.
- Form the negation by inserting 'not': '12 is not an even number'.
- Since the original statement is true, its negation must have the opposite truth value.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Where do I insert 'not' or 'no' in a statement?
Insert it right before the main verb or key claim of the sentence, e.g. '6 is a factor of 24' becomes '6 is not a factor of 24'.
The negation should read naturally while completely reversing the original claim.
Does negating a statement twice bring back the original meaning?
Yes, negating a statement twice returns a sentence with the same truth value as the original statement, since each negation flips the truth value once, and two flips cancel out back to the starting truth value.
Can a statement have more than one correct negation?
Different wordings can express the same negation correctly, as long as the truth value is fully reversed and the mathematical meaning stays clear, for example 'not' and 'no' can sometimes both be used depending on how the sentence is phrased.