Logical Reasoning

Quantifier

A word such as “all” or “some” stating how many cases a statement covers.

EnglishQuantifier
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中文量词

How it is used

In "all even numbers are divisible by 2", the quantifier is "all". Adding a quantifier turns an open sentence into a statement with a truth value: this one is true, whereas "some prime numbers are even" (quantifier "some") is also true, shown by 2.

Where it shows up in SPM

Quantifiers appear in the statements part of Form 4 Logical Reasoning. Paper 1 asks for the truth value of an "all" or "some" statement, or its negation.

Paper 2 links quantifiers to counter-examples when testing whether a general statement holds.

Don't confuse it with

NegationA quantifier states how many cases a statement covers; negation is the separate step of reversing that statement, which also switches "all" to "some ... not".

Open the chapter: Logical Reasoning →

Frequently asked questions

What is the difference between "all" and "some"?

"All" claims every case fits, so one exception makes it false. "Some" claims at least one case fits, so a single example makes it true.

"All primes are odd" is false (because of 2), but "some primes are odd" is true.

How do I disprove an "all" statement?

Find one counter-example. To disprove "all quadrilaterals have four equal sides", give a rectangle, which has four sides but not all equal.

A single exception is enough to make any "all" statement false.

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