difference between P[min(X1, X2, X3) < 3] and P[max(X1, X2, X3) < 3]

So what exactly is the difference between P[min(X1, X2, X3) < 3] and P[max(X1, X2, X3) < 3]. I am trying to solve problems 4 and 5 from the ACTEX P/1 Study Manual 2010 Edition page 211. The way i see it is

P[min(X1, X2, X3) < 3] = P(X1 < 3)*P(X2 < 3)*P(X3 < 3)

which is the same as

P[max(X1, X2, X3) < 3] = P(X1 < 3)*P(X2 < 3)*P(X3 < 3)

The solution guide used the survival function for the min, which i dont understand why it couldnt be done my approach. the solution for the max was the way i have it written. it is a uniform distribtion by the way.