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Answer :
Final answer:
The equivalent expression for "Not all integers are numbers" is "Some integers are not numbers." The negation of this statement is "All integers are numbers." Both interpretations maintain clarity in terms of universal and existential quantifiers.
Explanation:
Equivalent Expression and Negation of Quantified Statement
The original statement, "Not all integers are numbers," can be rephrased equivalently. This means we want to express it in a way that conveys the same meaning using standard logic terms.
Part A: Equivalent Expression
The correct equivalent expression for the statement is: Some integers are not numbers. This means there exists at least one integer that does not qualify as a number.
Part B: Negation of the Statement
The negation of the original statement can be framed clearly and is: All integers are numbers. This means that every integer qualifies as a number, opposing the idea that there are integers that are not numbers.
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Rewritten by : Batagu
