Writing formal propositions

Task number: 2782

First write the following propositions using quantifiers. Then negate them, and finally write the negated propositions informally, like the original propositions.

  • Variant 1

    All natural numbers are even.

  • Variant 2

    Every prime number is odd.

  • Variant 3

    Some natural number is divisible by all primes.

  • Variant 4

    Between \(n\) and \(2n\) we can always find some prime number.

Difficulty level: Easy task (using definitions and simple reasoning)
Proving or derivation task
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