Maths · Sets and their representation
Write negation of: All natural numbers are integers and all integers are not nat
Write negation of: All natural numbers are integers and all integers are not natural numbers.
- A. All natural numbers are not integers and all integers are not natural numbers
- B. All natural numbers are integers and all integers are natural numbers.
- C. Some natural numbers are integers and all integers are not natural numbers.
- D. All natural numbers are not integers and some integers are natural numbers.
Step-by-step solution
The negation of a conjunction (P ∧ Q) is ¬P ∨ ¬Q. The negation of 'All natural numbers are integers' is 'Some natural numbers are not integers' (or 'All natural numbers are not integers' in a stronger sense). The negation of 'All integers are not natural numbers' is 'Some integers are natural numbers'. Therefore, the correct negation is 'All natural numbers are not integers and some integers are natural numbers' (Option D).