Respuesta :
The answer is no, and the below explanation is given with a counter-example.
What is meant by an integer?
An integer is a number that includes both negative and positive numbers, including zero. It has no decimal or fractional parts. Here are a few examples of integers: -5, 0, 1, 5, 8, 97, and 3,043
P(n) is a condition that is true for P(0), P(1), and P(2), but P(3k) is true when P(k) is true for all numbers k0.
P(n) is thus not always true for all nonnegative integers n because 4 is not a multiple of 3.
For example, consider the property P(n): "n is 0 or 1, or n is a multiple of 3." Then P(0), P(1), and P(2) are trivially true, however, P(3k) is true for all numbers k because 3k is a multiple of 3. However, P(4) is false because 4 is not a multiple of 3.
As a result, no.
To know more about integers, visit:
https://brainly.com/question/15276410
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The complete question is:
"Suppose P(n) is a property such that 1. P(0), P(1), P(2) are all true, 2. for all integers k≥0, if P(k) is true, then P(3k) is true. Must it follow that P(n) is true for all integers n≥0?
If yes, explain why; if no, give a counterexample".
