Logical Reasoning · 3.1.1
Statements and truth values
Students must recognise whether a given sentence is a statement, one that can be judged as either true or false, but not both. They then explain what the sentence means in their own words and decide, based on mathematical or general facts, whether it is true or false.
The official learning standard (3.1.1)
“Explain the meaning of a statement and hence determine the truth value of a statement.”
What it means
Students must recognise whether a given sentence is a statement, one that can be judged as either true or false, but not both. They then explain what the sentence means in their own words and decide, based on mathematical or general facts, whether it is true or false.
How it is examined
This is examined in Paper 1 as short objective questions, usually giving several sentences and asking students to identify which one is a mathematical statement, or giving a single sentence and asking whether its truth value is true or false.
Worked example
Determine whether the sentence '15 is a multiple of 3' is a statement, and state its truth value.
- Check whether the sentence can be judged as either true or false: '15 is a multiple of 3' can be checked and is either true or false, so it is a statement.
- Recall that a multiple of 3 is a number that can be divided exactly by 3.
- Check: 15 ÷ 3 = 5, which is a whole number, so 15 is indeed a multiple of 3.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Is 'x + 5 = 8' a statement?
No, on its own it is not a statement, because its truth value depends on the unknown value of x, it could be true (if x = 3) or false for any other value, so it cannot be fixed as definitely true or definitely false.
Is a question like 'Is 7 a prime number?' a statement?
No, questions are never statements, because a statement must be a sentence that makes a claim which can be judged true or false, a question asks something rather than claiming something, so it has no truth value at all.
Can a statement be neither true nor false?
No, by definition, every statement must be exactly one of true or false, never both and never neither. If a sentence cannot be judged this way, it does not qualify as a mathematical statement in the first place.