Question

a. express the quantified statement in an equivalent way, that is, in a way that has exactly the same meaning.
b. write the negation of the quantified statement. (the negation should begin with \all,\ \some,\ or
o.\)
all computers are not smart.
a. express the quantified statement in an equivalent way.
○ a. not all computers are smart.
○ b. all computers are not smart.
○ c. at least one computer is smart.
○ d. no computer is smart.
b. write the negation of the quantified statement.
○ a. no computers are smart.
○ b. some computers are not smart.
○ c. some computers are smart.
○ d. all computers are not smart.

Explanation:

• For part a: "All computers are not smart" is equivalent to "Not all computers are smart". The original statement means that it's not the case that every single computer is smart.
• For part b: The negation of "All computers are not smart" (which is equivalent to "Not all computers are smart") is "Some computers are smart". When we negate a statement about the non - existence of a property for all elements in a set (computers in this case), we are saying that there exists at least one element in the set that has the property.

Answer:

a. A. Not all computers are smart.
b. C. Some computers are smart.