We will be applying Boundary Value Analysis to generate test cases.  The expected output can be  [Invalid date, previous Date].

Program:

#include<conio.h>
#include<stdio.h>
void main()
{
	int month,date,year, valid=-1,leap_year=-1;
	printf("please enter a date = ");
	scanf("%d",&date);
		printf("please enter a month = ");
	scanf("%d",&month);
		printf("please enter a year = ");
	scanf("%d",&year);
	if((date>0 && date<=31)&&(month>=1 && month<=12)&&(year>=2000 && year<=2050))
	{
	// finding given input is a leap year or not
	if((year%4)==0)
	{
		leap_year=1;
    if((year%100)==0)
    {
	if((year%400)==0)
	{
		leap_year=1;	
	}
	else
	{
	leap_year=-1;	
	}
}
}
if(month==2 && leap_year==1 && date >29)
valid=-1;
else if(month==2 && leap_year==-1 && date >28)
valid=-1;
else 
valid=1;
}

if((month==6 || month==4||month==9||month==11) && date>30)
valid=-1;

// validating & finding output


if(valid==1)
{
	printf("Entered date = %d-%d-%d",date,month,year);

if(date==1)
{
if(month==1)
{
date=31;
month=12;
year--;
}
else if(leap_year=1 && month==3)
{
	date=29;
	month--;
}
else if(leap_year==-1 && month==3)
{
	date=28;
	month--;
}
else if(month==2||month==4||month==6||month==8||month==9||month==11){
	date=31;
	month--;
}else{
	date=30;
	month--;
}
}
else{
	
	date--;
}
printf("\nPrevious date = %d-%d-%d \n",date,month,year);
}
else
printf("\n Not a valid date");

getch();
}

So, there will be 4N+ 1 test cases that is 4*3 +1 =13 in this case as we are using boundary value analysis.

Testing the program:

Invalid Date:

Previous Date: