Science:Math Exam Resources/Courses/MATH220/December 2011/Question 02 (a)
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Question 02 (a) 

For any natural number n, let P(n) be the statement "n is divisible by 4", and let Q(n) be the statement "n^{2}+1 is divisible by 3". Consider the statement Is this statement true or false? Prove your answer. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

You need to first determine whether the statement is true or false. How might you determine this? Is there some way to check specific cases? 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We note that P(4) is the statement "4 is divisible by 4", which is true. We also note that Q(4) is the statement "17 is divisible by 3" which is false. As such, the implication does not hold, and so the statement is false. 