Science:Math Exam Resources/Courses/MATH220/December 2011/Question 02 (a)/Solution 1

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

$\displaystyle P(4)\Rightarrow Q(4)$

does not hold, and so the statement

$\forall \,n\in \mathbb {N} ,P(n)\Rightarrow Q(n)$

is false.