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

For n ∈ 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". Write out in words the statement "P(3) → Q(4)", its converse, and its contrapositive. 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

The converse of the statement is 
Hint 2 

The contrapositive of the statement is 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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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is "3 is divisible by 4 implies that 17 is divisible by 3".
hence in words it is "17 is divisible by 3 implies that 3 is divisible by 4".
In words this is "17 is not divisible by 3 implies that 3 is not divisible by 4". 