Which number serves as a counterexample to the statement below:
All positive integers are divisible by 2 or 3
I need as much as possible.
its 25
To find a counterexample to the statement "All positive integers are divisible by 2 or 3," we need to find a positive integer that is not divisible by 2 or 3.
One way to approach this is by trying different positive integers and checking if they are divisible by both 2 and 3. However, this can be time-consuming.
An alternative approach is to consider the least common multiple (LCM) of 2 and 3, which is 6. Any positive integer that is not divisible by 6 would serve as a counterexample.
Let's look at the first few positive integers:
1: Not divisible by 2 or 3
2: Divisible by 2 but not 3
3: Divisible by 3 but not 2
4: Divisible by 2 but not 3
5: Not divisible by 2 or 3
6: Divisible by both 2 and 3
From the above analysis, we can see that the number 5 is not divisible by 2 or 3 and therefore serves as a counterexample to the given statement.
Here are the options:
A: 100
B: 57
C: 30
D: 25