Prove that there is a prime between n and n factorial

Let k = n! - 1. Well, since all numbers from 2 to n divide n!, none of these divides k. This means that k either a prime , in which case we are done, or there exists a prime p > n which divides n! - 1. In the latter case, p is between n and n factorial and p is prime, so the proof is complete.

since proposition states that a number is greater than 25, if is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted