Datecheck + Print In Various Options

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication25
{
    public delegate void isDateValid(int falseInfo, string falseType);
    enum Months : byte { January, February, March, April, May, June, July, August, September, October, November, December, False };
    public class Date
    {
        private int year;
        private Months month;
        private int day;
        private bool isFalse = false;
        public isDateValid dateCheck;
        public Date(int year, int month, int day)
        {
            this.year = year;
            if (month > 0 && month < 13)
            {
                this.month = (Months)month-1;
            }
            else
            {
                this.month = (Months)13;
                isFalse = true;
            }
                this.day = day;
        }
        public void DayMonthCheck()
        {
            if (month != (Months) 13)
            {
                if ((int)month > 2 && (int)month < 8)
                {
                    if ((int)month % 2 == 0)
                    {
                        if (day > 30)
                        {
                            dateCheck(day, "day");
                            isFalse = true;
                        }
                    }
                    else
                    {
                        if (day > 31)
                        {
                            dateCheck(day, "day");
                            isFalse = true;
                        }
                    }
                }
                else if ((int)month >= 8)
                {
                    if( (int) month % 2 == 0)
                    {
                        if (day > 31)
                        {
                            dateCheck(day, "day");
                            isFalse = true;
                        }
                    }
                    else
                    {
                        if (day > 30)
                        {
                            dateCheck(day, "day");
                            isFalse = true;
                        }
                    }
                }
                else if ((int)month == 1)
                {
                    if (day > 31)
                    {
                        dateCheck(day, "day");
                        isFalse = true;
                    }
                }
                else if ((int)month == 2)
                {
                    if (day > 28)
                    {
                        dateCheck(day, "day");
                        isFalse = true;
                    }
                }
            }
            else
                dateCheck((int)month, "month");
            if (day < 1)
            {
                dateCheck(day, "day");
                isFalse = true;
            }
        }
        public static void Sub()
        {
        }
        public void Print(int selectedOutput)
        {
            if (!isFalse)
            {
                if (selectedOutput == 1)
                    Console.WriteLine("{0}/{1}/{2}", day, (int)month+1, year);
                else if (selectedOutput == 2)
                    Console.WriteLine("{0} {1}, {2}", day, month, year);
                else if (selectedOutput == 3)
                    Console.WriteLine("{0} - {1} - {2}", day, (int)month+1, year);
                else
                    Console.WriteLine("{0}/{1}/{2}", (int)month+1, day, year);
            }
        }
    }
    class Program
    {
        static void Main(string[] args)
        {
            Console.Write("Year: ");
            int year = int.Parse(Console.ReadLine());
            Console.Write("Month: ");
            int month = int.Parse(Console.ReadLine());
            Console.Write("Day: ");
            int day = int.Parse(Console.ReadLine());
            Date today = new Date(year, month, day);
            today.dateCheck = new isDateValid(DateValidation);
            today.DayMonthCheck();
            Console.WriteLine("Choose printing method:");
            Console.WriteLine("1. dd/mm/yy\n2. dd Month, yy\n3. dd-mm-yy\n4. mm/dd/yy");
            int selectedOutput = int.Parse(Console.ReadLine());
            today.Print(selectedOutput);
        }
        static void DateValidation(int date, string type)
        {
            Console.WriteLine("Invalid date! {0} {1} doesn't exist.", type, date);
        }
    }
}