Question

Take for example the property or the unary relation, Man(x). It seems to "really" be a binary relation between x and {true, false} "under the hood." So would this make the notion of unary relations a more sophisticated shorthand for binary relations when the output is either true or false, i.e. are binary relations the building block of all relations and properties?

Answer 1

Unary relations in mathematics represent properties or attributes applied to a single object, without involving a binary relationship. They do not serve as a shorthand for binary relations when the output is either true or false.

Step-by-step explanation:

In mathematics, unary relations represent properties or attributes that are applied to a single object or element. They are not binary relations between x and {true, false} as suggested in the question.

Unary relations simply state whether an object possesses a certain property or not, without considering a binary relationship or output.

For example, the unary relation 'Man(x)' represents the property of being a man for an object x. If x is a man, the unary relation evaluates to true, and if x is not a man, it evaluates to false. It is important to note that unary relations are not a shorthand for binary relations, as they do not involve a binary relationship between x and {true, false}.