a. Statement: ∀ even integers n, ∃ an integer k such that n = 2k. b. Negation: ∃ an even integer n such that ∀ integers k, n $\neq$ 2k. There is some even integer that is not equal to twice any other integer.
Work Step by Step
Recall the negation of a for all statement: ~($\forall x$ in D, P(x)) $\equiv \exists x$ in D such that ~P(x). Recall the negation of an exists statement: ~($\exists x$ in D, P(x)) $\equiv \forall x$ in D such that ~P(x). To negate a multiply quantified statement, apply the laws in stages moving left to right along the sentence.