Sort each English claim by the quantifier it uses.
Groups: Universal claim · Existential claim
- There is a number that divides every integer
- At least one student in the class studies Latin
- Every prime greater than 2 is odd
- Each vertex of this graph has even degree
- No integer is both even and odd
- Some integer is both even and prime
Hints
- Ask whether the claim is about every member of the domain or about the existence of at least one.
- A claim beginning 'no' is a universal one in disguise: it says every member fails the property.
Show the answer
Universal claim: Every prime greater than 2 is odd, No integer is both even and odd, Each vertex of this graph has even degree
Existential claim: Some integer is both even and prime, There is a number that divides every integer, At least one student in the class studies Latin
'Every', 'each' and 'no' are all universal, 'no integer is both even and odd' says that for all x, x is not both. 'Some', 'there is' and 'at least one' are existential. Filing a 'no' statement as existential because it feels negative is the trap; the negation of an existential is a universal, which is exactly what 'no' expresses.
Practise Predicate Logic and Quantifiers
The app has 4 more questions on this lesson, and keeps your place in the course. Computer Science I is free to start.
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