logic1 http://www.openmath.org/cd/logic1.ocd 2003-04-01 2001-03-12 2 0 official quant1 relation1 This CD holds the basic logic functions. equivalent This symbol is used to show that two boolean expressions are logically equivalent, that is have the same boolean value for any inputs. The condition (A is equivalent to B) is equivalent to the condition that (A implies B and B implies A) not This symbol represents the logical not function which takes one boolean argument, and returns the opposite boolean value. for all x | not(not(x))=x and This symbol represents the logical and function which is an n-ary function taking boolean arguments and returning a boolean value. It is true if all arguments are true or false otherwise. for all x | x and not(x) = false xor This symbol represents the logical xor function which is an n-ary function taking boolean arguments and returning a boolean value. It is true if there are an odd number of true arguments or false otherwise. for all x | x xor x = false for all x | x xor not(x) = true or This symbol represents the logical or function which is an n-ary function taking boolean arguments and returning a boolean value. It is true if any of the arguments are true or false otherwise. for all x | x or not(x) = true for all a,b | not(a and b)= (not(a) or not(b)) implies This symbol represents the logical implies function which takes two boolean expressions as arguments. It evaluates to false if the first argument is true and the second argument is false, otherwise it evaluates to true. for all x | false implies x true This symbol represents the boolean value true. not true = false false This symbol represents the boolean value false. not false = true