Problem Solving

The function f is defined for all positive integers n by the following rule:
f(n) is the no of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is a prime no then f(p) =

A) p-1
B) p-2
C) (p+1)/2
D) (p-1)/2
E) 2

Can someone give a detailed insight ??? Thank you

Is the answer A ?

reason:
Try any prime number say 3: the number of positive integers less than 3 is 2 and all numbers less than the prime number selected will have only 1 as a common factor with the prime number selected.

e.g.
Number 5 : 1,2,3,4
Number 7 : 1,2,3,4,5,6

Is it B?

p=3, f(p) = 1 (Factors 2 only)
p=5, f(p) = 3 (Factors 2, 3, and 4)
p = 7, f(p) = 5 (Factors 2,3,4,5,6)

Therefore f(p) = p-2

A?

Please check https://www.beatthegmat.com/viewtopic.php?t=3627