Determining which statement is true

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In summary, the conversation discusses various statements regarding the divisibility of a fixed positive integer n by 6 and 3. The first statement is proven to be true by choosing the values 12 and 18 for n, while the second statement is questioned with the example of n=9. The third statement involves n^2 and is considered true based on the example of n=6. The conversation concludes with a suggestion to find a chain of assumptions and proofs or a disproving example to verify or falsify the assumptions.
  • #1
ver_mathstats
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We are given several statements and we must determine which one is true, n is a fixed positive integer, it asks which statement is true regardless of which positive integer n you choose?

The first one states that if n is divisible by 6, then n is divisible by 3.
I chose 12 for n and it was true.
I chose 18 for n and it was true as well.
Does this mean that the statement is true? Because I believe it is true.

Another one states if n is divisible by 3, then n is divisible by 6.
This one is still true because if you substitute 12 and 18 it still holds true.

Another one also states that if n2 is divisible by 6, then n is divisible by 6.
I chose 6 for n and it held true, ((6)2)/6 and 6/6 worked out meaning it must be true.

Is this the correct way to solve this question or am I doing it incorrectly?

Thank you.
 
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  • #2
ver_mathstats said:
We are given several statements and we must determine which one is true, n is a fixed positive integer, it asks which statement is true regardless of which positive integer n you choose?

Is this the correct way to solve this question or am I doing it incorrectly?

Good morning,

first of all, if this is some kind of homework please use the homework forum with its template. Secondly, it doesn't suffice to prove a mathematical statement with two examples, so I think you should find a proof, which applies for the infinity of numbers (or one converse example for disprooving).

ver_mathstats said:
The first one states that if n is divisible by 6, then n is divisible by 3.
I chose 12 for n and it was true.
I chose 18 for n and it was true as well.
Does this mean that the statement is true? Because I believe it is true.

Assumption: ##n\;mod\;6 = 0 \rightarrow n\;mod\;3 = 0##
##6 = 2\cdot 3##
##\frac{n}{6} = \frac{n}{2\cdot 3} = \frac{1}{2}\frac{n}{3} \rightarrow \frac{n}{3}\;mod\;2 = 0##
The modulo of a number only can be zero, if it is integral, therefore ##\frac{n}{3}## must be an integral and ##n\;mod\;3 = 0##

ver_mathstats said:
Another one states if n is divisible by 3, then n is divisible by 6.
This one is still true because if you substitute 12 and 18 it still holds true.

What about the ##n=9##?

ver_mathstats said:
Another one also states that if n2 is divisible by 6, then n is divisible by 6.
I chose 6 for n and it held true, ((6)2)/6 and 6/6 worked out meaning it must be true.

Try by yourself. Find a chain of assumptions and proofs or one disprooving example to verify or falsify the assumption.
 
  • #3
stockzahn said:
Good morning,

first of all, if this is some kind of homework please use the homework forum with its template. Secondly, it doesn't suffice to prove a mathematical statement with two examples, so I think you should find a proof, which applies for the infinity of numbers (or one converse example for disprooving).
Assumption: ##n\;mod\;6 = 0 \rightarrow n\;mod\;3 = 0##
##6 = 2\cdot 3##
##\frac{n}{6} = \frac{n}{2\cdot 3} = \frac{1}{2}\frac{n}{3} \rightarrow \frac{n}{3}\;mod\;2 = 0##
The modulo of a number only can be zero, if it is integral, therefore ##\frac{n}{3}## must be an integral and ##n\;mod\;3 = 0##
What about the ##n=9##?
Try by yourself. Find a chain of assumptions and proofs or one disprooving example to verify or falsify the assumption.

I was unaware of the homework template, I shall start using that now, my apologies. Thank you for the help. I am going to retry the question right now.
 
  • #5

1. What is the process for determining which statement is true?

The process for determining which statement is true involves gathering evidence, analyzing data, and making logical conclusions based on the evidence. This can include conducting experiments, researching previous studies, and using critical thinking skills.

2. How do you know if a statement is true or false?

The truth of a statement can be determined by evaluating the evidence and reasoning behind it. If the evidence is reliable and the reasoning is logical, then the statement is more likely to be true. However, it is important to always question and critically evaluate information before accepting it as true.

3. What are some common fallacies that can lead to incorrect statements being perceived as true?

Some common fallacies that can lead to incorrect statements being perceived as true include confirmation bias, where we only seek out information that confirms our beliefs, and false cause and effect, where we assume that one event caused another without proper evidence.

4. How do you determine the credibility of a source when evaluating a statement?

To determine the credibility of a source, it is important to consider factors such as the author's credentials, the publication or website where the information is found, and whether the information is supported by other reliable sources. It is also important to be aware of potential biases or conflicts of interest that may affect the credibility of a source.

5. Can a statement ever be considered 100% true?

While it is possible for a statement to be supported by overwhelming evidence and widely accepted as true, it is important to remember that our understanding of the world is constantly evolving and new evidence can always emerge. Therefore, it is generally not considered accurate to say that a statement is 100% true, as there is always the possibility of new information or perspectives that may challenge it.

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