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In Mathematics / Middle School | 2014-11-06

Cynthia made the conjecture that the sum of any prime number and any composite number is a composite number.

Which equation is a counterexample to her conjecture?

A. 11 + 2 = 13

B. 5 + 8 = 13

C. 13 + 2 = 15

D. 11 + 9 = 20

Asked by Kaylee123

Answer (2)

Well,
We will need an equation in the form of: (prime no.) + (composite no.) = (prime no.)
Options C and D immediately are rejected because the result is a composite number.
Option A looks like it could be a counterexample, but 2 is a prime number.
That leaves option B, which is the correct option.

Answered by SchwarzschildRadius | 2024-06-10

The conjecture states that the sum of a prime and a composite number is composite. None of the given options successfully serve as a counterexample because they do not provide a sum that is prime when a prime is added to a composite. Therefore, the conjecture is not disproven by the provided examples.
;

Answered by SchwarzschildRadius | 2024-12-26

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