Logical Reasoning · Form 4
What counts as a statement?
In this chapter a statement is a sentence that is either definitely true or definitely false, but never both at once. Questions, commands and personal opinions are not statements, because you cannot fairly label them true or false.
A statement carries a truth value
The test is simple: can the sentence be judged true or false? 'Seven is a prime number' is a statement (true), and 'Nine is a multiple of four' is also a statement (false).
Both qualify because each can be labelled with one truth value, even though one of them turns out to be wrong.
Why questions, commands and opinions don't count
'Is seven a prime number?' asks something rather than asserting it, so it has no truth value.
'Add three and five' is a command, and 'Mathematics is enjoyable' is an opinion, neither can be pinned down as true or false for everyone. A sentence with an unknown, such as 'x + 2 = 5', is also not a statement until you know what x is, because its truth depends on the value of x.
The mistake to avoid
Many students think a false sentence cannot be a statement, so they reject '3 + 4 = 8'. But that sentence is a perfectly good statement, just a false one.
What matters is not whether the sentence is correct, but whether it can be decided true or false at all.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I tell whether a sentence is a statement in a maths exam question?
Check if the sentence can be judged true or false with certainty, using only the information given. "5 is a prime number" is a statement (true); "Is 5 a prime number?"
and "5 is a nice number" are not, since a question and an opinion can't be marked true or false.
Why isn't "x + 2 = 5" always counted as a statement?
Because its truth depends on the unknown value of x, it isn't fixed true or false until x is given a value. It only becomes a statement once x is replaced by a specific number, such as x = 3, which makes it true.
What's a common mistake students make when identifying statements in Paper 1?
Treating exclamations, instructions or vague opinions ("this is hard!") as statements.
Exam questions test this precisely by mixing in a command or a question among true/false sentences, always ask whether the sentence itself, not your feeling about it, can be judged true or false.