Rational numbers are numbers that can be expressed as the quotient of two integers (with the denominator not equal to zero). Natural numbers are the positive integers (1, 2, 3, ...).
Looking at the provided sets:
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Set 1: 3 1/2, -4, 4/7, 1
- Contains 3 1/2 (a rational number), -4 (a rational number), 4/7 (a rational number), and 1 (a natural number).
- This set includes natural numbers (1), so it does not meet the criteria.
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Set 2: -1, 0, 1, 2
- Contains -1 (a rational number), 0 (a rational number), 1 (a natural number), and 2 (a natural number).
- This set includes natural numbers (1, 2), so it does not meet the criteria.
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Set 3: 3, 4, 5, 6
- Contains 3, 4, 5, and 6, all of which are natural numbers.
- This set includes only natural numbers, so it does not meet the criteria.
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Set 4: 1/4, -4, 10/7, 3
- Contains 1/4 (a rational number), -4 (a rational number), 10/7 (a rational number), and 3 (a natural number).
- This set includes a natural number (3), so it does not meet the criteria.
None of the sets provided entirely consist of rational numbers excluding natural numbers, but Set 1 and Set 4 have natural numbers included.
Assuming you are looking specifically for rational numbers, Set 2 (-1, 0) has rational numbers, but also includes natural numbers.
To summarize, none of the provided sets meet the criteria of being exclusively rational without any natural numbers. If forced to choose one, Set 1 and Set 4 both have the most rational numbers, with one being a natural number. You'll need to consider changing the sets to find one that meets that specific request.
1 answer