Write a sentence of predicate logic which intuitively holds in a model iff the model has (respectively)
(a) exactly three distinct elements
(b) at most three distinct elements
Predicate logic is a formal system of logic that involves statements or propositions about objects and their properties. It is used to represent and reason about relationships between different objects or concepts.
While propositional logic deals with simple statements and their truth values, predicate logic expands on this by including variables, predicates, and quantifiers to express more complex relationships between objects.
A predicate is a statement that expresses a property or characteristic of an object. It is denoted by a symbol and is usually followed by one or more variables.
Quantifiers are symbols used in predicate logic to indicate the scope or extent of a statement. There are two types of quantifiers: universal quantifiers (∀) and existential quantifiers (∃). These symbols are used to make statements about all or some objects in a given domain.
To understand a predicate logic question, break it down into its components: the variables, predicates, and quantifiers. Identify the subject and the property being described, and determine the logical relationship between them. It may also be helpful to draw a diagram or create a truth table to visualize the logic.