The following statement is false. r: All humans are taller than seven feet. Use the representation of $$ r $$ to express the symbolic statement $$ \sim $$ in words. Verbal statements should begin with "all," "some," or "no." What can you conclude about the resulting verbal statement? Choose the statement below that expresses the symbolic statement $$ \sim $$ r in words. A. Some humans are taller than seven feet. B. Some humans are not taller than seven feet. C. All humans are shorter than 12 feet. D. No humans are taller than seven feet. What can you conclude about the resulting verbal statement?

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The symbolic statement $$ \sim r $$ is expressed as "Some humans are not taller than seven feet." The correct choice is B. This indicates that the negation of a universal statement leads to an existential statement. The statement $$ r $$ is "All humans are taller than seven feet." The negation of this statement, represented as $$ \sim r $$, would be "It is not the case that all humans are taller than seven feet." To express $$ \sim r $$ in words, we can say: "Some humans are not taller than seven feet." This corresponds to option B. So, the correct choice is: **B. Some humans are not taller than seven feet.** Regarding the conclusion about the resulting verbal statement, we can infer that the negation of a universal statement (like "all") leads to an existential statement (like "some"). In this case, the negation indicates that there exists at least one human who does not meet the original condition of being taller than seven feet.

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