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Exercise 1.3 · Q94

Q.Write the negation of the following statement: All natural numbers are whole numbers.

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'All natural numbers are whole numbers' is the universal statement ∀n∈N\forall n\in N, nn is a whole number. Negating a universal quantifier gives an existential quantifier with the inner statement negated: ∼[∀n∈N,P(n)]≡∃n∈N\sim[\forall n\in N, P(n)]\equiv \exists n\in N such that ∼P(n)\sim P(n). So the negation is: 'T …

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