Logical Reasoning
Negation
The opposite of a statement, which reverses its truth value.
| English | Negation |
|---|---|
| Bahasa Melayu | Penafian |
| 中文 | 否定 |
How it is used
The negation of "12 is divisible by 5" is "12 is not divisible by 5". The original is false, so its negation is true.
In symbols, if p is a statement, its negation is written ~p.
Where it shows up in SPM
Negation appears early in Logical Reasoning (Form 4), often in Paper 1 as "write the negation of" or "which is the negation of". It also underpins Paper 2 truth tables and the negation of quantifiers such as turning "all" into "some ...
not".
Don't confuse it with
Open the chapter: Logical Reasoning →
Frequently asked questions
How do I negate a statement with "is"?
Insert "not" so the meaning is reversed. The negation of "81 is a perfect square" is "81 is not a perfect square".
Since 81 = 9², the original is true and the negation is false. Keep the rest of the sentence the same.
What is the negation of "all" and "some"?
The negation of "all A are B" is "some A are not B", and the negation of "some A are B" is "no A are B". For example, negating "all multiples of 4 are even" gives "some multiples of 4 are not even".
Does negating a statement twice return the original?
Yes. Negating twice, ~(~p), gives back p with the same truth value.
The negation of "7 is odd" is "7 is not odd", and negating that again returns "7 is odd", which is true throughout.