Subjects logic

Negation Statement B17460

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1. The problem asks for the negation of the statement: "All COVID-19 patients have pneumonia." 2. The original statement is a universal statement: "For all COVID-19 patients, they have pneumonia." Symbolically, this is $\forall x, P(x)$ where $P(x)$ means "x has pneumonia." 3. The negation of a universal statement $\forall x, P(x)$ is an existential statement $\exists x$ such that $\neg P(x)$. In words, this means "There exists at least one COVID-19 patient who does not have pneumonia." 4. Among the options, Option A states: "Some COVID-19 patients do not have pneumonia," which matches the negation. 5. Therefore, the negation of "All COVID-19 patients have pneumonia" is Option A: "Some COVID-19 patients do not have pneumonia."