question about time conversion

I was wondering if someone could tell me what is wrong with this code. I am trying to write a program which will ask the user to enter a time and then add 12 to it if the end char entered is P and the numerical value of the hour is < 12. With the following code, the program adds 12 regardless and I am trying to figure out how to resolve this. Thanks.

Code:

cout << "Enter start time (hh:mm A/P): ";

float start_hour = 0;
float start_minute = 0;

char A = 0;
char P = 0; 
char dummy(0);

cin >> start_hour >> dummy >> start_minute >> A || P;

if ( P && start_hour <12 );
	                       {
	                          start_hour = start_hour + 12;
						   }

What's A || P supposed to mean?

What's the ; at the end of the if statement do?

The answer to both is "not what you're expecting"