A predicate can be described as… (Pick the statement that applies.)

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BlackTom AI · Accepted Answer

This question asks us to identify what a predicate can be described as among the given statements.
Option a: 'A proposition whose domain is {True, False}.' A proposition is typically a statement that is either true or false, not a function with a domain. The idea of a domain applies to functions, so calling a proposition to have a domain {True, False} is a category error. This makes this option incorrect because it mislabels the object as a proposition rather than a function.
Option b: 'A function whose domain is {True, False}.' A predicate is not typically described as having a domain consisting of the truth values themselves. In logic, predicates take elements from some domain (like natural numbers, people, etc.) and return a truth value. Stating that the domain is {True, False} reverses the usual perspective and is therefore inaccurate for the standard notion of a predicate.
Option c: 'A proposition whose codomain is {True, False}.' A proposition is already a truth value (true or false) rather than a function with a codomain. Saying a proposition has codomain {True, False} conflates the idea of a proposition with a function output. This makes the option incorrect because it assigns a functional-coding role to something that is simply a statement with a truth value.
Option d: 'A function whose codomain is {True, False}.' This aligns with the standard definition of a predicate in logic: a predicate is a function that maps elements of some domain to truth values, i.e., its codomain is the set {True, False}. The function perspective correctly captures the idea that a predicate assigns true or false to each input from its domain, which is the hallmark of a propositional function.
Thus, option d is the most accurate description of a predicate, while the other options mix up the roles of propositions and functions or misstate the domain/codomain relationships.

FIT1058_S1_2025 Week 5 Pre-reading Quiz

A predicate can be described as… (Pick the statement that applies.)

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