I’ve been reading about propositional (or sentential) logic in the book “The Annotated Turing”. I put together a quick console app to write out truth tables. It helped me get the hang of the mathematical notation “v”, “&”, and “->”. In C# those would be ||, &&, and !x || y respectively. I hope someone else finds it useful.

using System;
using System.Collections.Generic;

namespace PropositionalLogic
{
    public class Program
    {
        public class truthvalue
        {
            public bool X { get; set; }
            public bool Y { get; set; }
        }

        public static bool XorY(bool x, bool y)
        {
            return (x || y);
        }

        public static bool XandY(bool x, bool y)
        {
            return (x && y);
        }

        public static bool Exclusive(bool x, bool y)
        {
            return (x && y) && !(x && y);// always false
        }

        public static bool Tautoloty(bool x, bool y)
        {
            return x || y || (!x && !y);// always true
        }

        public static bool Contradition(bool x, bool y)
        {
            return x || (y && !y);
        }

        public static bool MaterialImplication(bool x, bool y)
        {
            return !x || y; //this can also be expressed as the following conjunction !(x && !y);
        }

        public static bool BiConditional(bool x, bool y)
        {
            return MaterialImplication(x, y) && MaterialImplication(y, x); //"if and only if"
        }

        static void Main(string[] args)
        {
            var truthTable = new List<truthvalue>
                                 {
                                     new truthvalue() {X = false, Y = false},
                                     new truthvalue() {X = false, Y = true},
                                     new truthvalue() {X = true, Y = false},
                                     new truthvalue() {X = true, Y = true}
                                 };

            var sentences = new Dictionary<string , Func<bool, bool, bool>>
                                {
                                    {"X v Y", XorY},
                                    {"X & Y", XandY},
                                    {"(x v y)& -(x & y)", Exclusive},
                                    {"x v y v (-x & -y)", Tautoloty},
                                    {"x -> y", MaterialImplication},
                                    {"x ~ y", BiConditional}
                                };

            CalculateTruthTable(truthTable, sentences);

            Console.ReadLine();
        }

        private static void CalculateTruthTable(IEnumerable<truthvalue> truthTable, Dictionary<string , Func<bool, bool, bool>> sentences)
        {
            foreach (var sentence in sentences)
            {
                Console.WriteLine("");
                Console.WriteLine("|X      |Y      |{0}  |", sentence.Key);

                foreach (var value in truthTable)
                {
                    var x = value.X;
                    var y = value.Y;

                    var result = sentence.Value(x, y);

                    Console.WriteLine("|{0}  |{1}  |{2}  |", PrettyPrint(x), PrettyPrint(y), PrettyPrint(result));
                }
            }
        }

        private static string PrettyPrint(bool input)
        {
            return input ? input + " " : input.ToString();
        }
    }
}