The great mathematician Countalot discovered the Incrediblenumbers; he does not know yet if they are finite or infinite,but he made the following conjecture:If they are infinite, then at least one of them has 8 distinctprime factors.One of his students, Countagain, showed that Countalot’sconjecture is false. Therefore he proved that:A. if Incredible numbers are finite, then none of them has 8distinct prime factorsB. if Incredible numbers are finite, then all of them have 8distinct prime factorsC. Incredible numbers are infiniteD. Incredible numbers are infinite and none of them has 8distinct prime factorsE. Incredible numbers are infinite and all of them have 8distinct prime factors22
Question
The great mathematician Countalot discovered the Incrediblenumbers; he does not know yet if they are finite or infinite,but he made the following conjecture:If they are infinite, then at least one of them has 8 distinctprime factors.One of his students, Countagain, showed that Countalot’sconjecture is false. Therefore he proved that:A. if Incredible numbers are finite, then none of them has 8distinct prime factorsB. if Incredible numbers are finite, then all of them have 8distinct prime factorsC. Incredible numbers are infiniteD. Incredible numbers are infinite and none of them has 8distinct prime factorsE. Incredible numbers are infinite and all of them have 8distinct prime factors22
Solution 1
The student, Countagain, disproved Countalot's conjecture which stated that "If Incredible numbers are infinite, then at least one of them has 8 distinct prime factors." This means that it is not true that if the Incredible numbers are infinite, then at least one of them has 8 distinct prime factors.
However, this does not provide any information about whether the Incredible numbers are finite or infinite. It only tells us that if they are infinite, it is not guaranteed that at least one of them has 8 distinct prime factors.
Therefore, the correct answer is not given in the options A to E. The conclusion that can be drawn from Countagain disproving Countalot's conjecture is:
F. If Incredible numbers are infinite, it is not guaranteed that at least one of them has 8 distinct prime factors.
Solution 2
No answer
Solution 3
The student, Countagain, disproved Countalot's conjecture. This means that even if the Incredible numbers are infinite, it's not guaranteed that at least one of them has 8 distinct prime factors. Therefore, the correct answer is:
D. Incredible numbers are infinite and none of them has 8 distinct prime factors.
Solution 4
The student, Countagain, disproved Countalot's conjecture. This means that even if the Incrediblenumbers are infinite, it's not guaranteed that at least one of them has 8 distinct prime factors. Therefore, the correct answer is:
D. Incredible numbers are infinite and none of them has 8 distinct prime factors.
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