Consider the statement P: “If an integer n is divisible by 4, then n + 2 is also divisible by 4.” Examine this claim and respond to the following.
(i) Calculate n + 2 for n = 4, 8 and 12. For each value, state whether the result is divisible by 4.
(ii) Based on your observations in part (i), decide whether P appears to be always true. If you suspect it is false, find one integer value of n that contradicts P.
(iii) Give a brief justification showing why the single value obtained in part (ii) is enough to disprove the original statement P for all integers.