Practice question · Sort into groups
Sort each statement by the quantifier it genuinely needs.
Groups: Universal (for all) · Existential (there exists)
- No integer is both even and odd
- At least one even number is prime
- Every prime above 2 is odd
- Some integer is its own square
- Each square is non-negative
Hints
- 'Every', 'each' and 'no' all range over the whole domain.
- 'No x is P' is universal in disguise: for all x, NOT P(x).
Show the answer
Universal (for all): Every prime above 2 is odd, No integer is both even and odd, Each square is non-negative
Existential (there exists): Some integer is its own square, At least one even number is prime
Why
'Every', 'each' and 'no' are universal, note that 'no integer is both even and odd' means 'for all x, NOT(...)'. 'Some' and 'at least one' are existential, each satisfied by a single witness (x = 0 or 1, and 2 respectively).
Practise Quantifiers and Predicates
The app has 5 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
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