Predicate Logic Quiz: Propositional Logic Schema Operators

Questions and Answers

The proposition 'There exists an x in the universe of discourse such that P(x) is true'

For all values in the universe, the predicate is true

$\exists xP(x)$

The predicate is true for some, but not necessarily all, choices of values Signup and view all the answers

$\forall$ Signup and view all the answers

$P(x)$ will be true for some values of $x$ or $Q(x)$ will be true for some values of $x$ Signup and view all the answers

The predicate is true whatever values are chosen Signup and view all the answers

By filling the spaces with values or choosing values for variables Signup and view all the answers

$\exists xP(x)$ Signup and view all the answers

The sum of any two elements x and y is greater than 10 Signup and view all the answers

Study Notes

Logic is the study of reasoning and the validity of arguments, concerned with the truth of statements (propositions) and the nature of truth.
Formal logic is concerned with the form of arguments and the principles of valid inference.

Propositional logic is the study of propositions, which are declarative statements that can result in either true or false.
Propositions may be combined with other propositions using logical connectives to form compound propositions.
Propositional logic can be used to encode simple arguments expressed in natural language and to determine their validity.

Five propositional connectives, in descending order of operator precedence:
Truth tables are used to determine whether a propositional statement is true or false for all possible instances of the variable.

The implication p=>q is true in every case except when p is true and q is false.
The implication p=>q is true if and only if we can prove q by assuming p.

A negation of a proposition is true when the original proposition is false, and false when the original proposition is true.
Tautologies are propositions that evaluate to true in every combination of their propositional variables.
Contradictions are propositions that evaluate to false in every combination of their propositional variables.

Predicate logic is a richer system than propositional logic, allowing complex facts about the world to be represented.
Predicate calculus consists of predicates, variables, constants, and quantifiers.

A predicate is a statement that contains variables (predicate variables), which may be true or false depending on the values of these variables.
The domain of a predicate variable is the collection of all possible values that the variable may take.

The universal quantifier states that a predicate is true for all possible values in the universe of discourse.
The existential quantifier states that there exists a value in the universe of discourse for which a predicate is true.

A predicate with free variables or 'spaces' is neither true nor false until values are chosen for these variables or the spaces are filled.
A predicate that is true for all choices of values is said to be valid.
A predicate that is true for some, but not necessarily all, choices of values is said to be satisfiable.