Predicate Symbols, Arity, and Open Statements Quiz

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 7387 | Total Attempts: 9,527,684
| Questions: 15 | Updated: Dec 1, 2025
Please wait...
Question 1 / 15
0 %
0/100
Score 0/100
1) Which of the following shows an application of a predicate symbol?

Explanation

A predicate symbol is a letter that represents a property or relation that can be applied to an argument. In option (b), we are applying P to the argument x. The other options are equations or complete statements, not predicate applications.

Submit
Please wait...
About This Quiz
Predicate Statements Quizzes & Trivia

Are you ready to get comfortable with predicate statements in formal logic? This quiz focuses on the basics of how predicates work and how they differ from full propositions. You’ll practice recognizing predicate symbols like P(x) and R(x, y), identifying arity (how many arguments a predicate takes), and distinguishing between... see moreopen predicates with free variables and closed statements with definite truth values. You’ll also work through examples that use domains (such as integers or students), learn how to express relations like “x is greater than y” using predicate notation, and see how negation affects a predicate (for example, turning “x is positive” into “x ≤ 0”). By the end of this quiz, you’ll be better at reading, writing, and interpreting predicate statements as the building blocks of predicate logic. see less

2)
You may optionally provide this to label your report, leaderboard, or certificate.
2) What does P(x) represent in predicate logic?

Explanation

In predicate logic, P(x) represents a statement that says the object x has the property P. For example, if P stands for "is even", then P(x) means "x is even". It does not represent a specific  value, a function, or a constant.
Submit
3) Which represents “x is greater than 5” using a predicate symbol?

Explanation

A predicate symbol is a letter (like G) that represents a relation. The statement "x is greater than 5" involves a relation between x and 5, so we use a predicate symbol G with two arguments: G(x,5). Option b uses infix notation but not a predicate symbol explicitly. Option c uses a unary predicate, which would represent a property of x alone, not a relation between x and 5.
Submit
4) Negation of P(x) in direct syntactic form:

Explanation

The negation of a statement P(x) is written by placing the negation symbol ¬ in front of it, resulting in ¬P(x). This means "it is not the case that P(x)". The other options are incorrect: P(¬x) applies the predicate to the negation of x, which is not the same as negating the entire statement.
Submit
5) “x does not satisfy P” is:

Explanation

The statement "x is not even" is the negation of "x is even". Since P(x) means "x is even", we write the negation as ¬P(x). The other options are incorrect: P(¬x) would mean "the negation of x is even", which doesn't make sense.
Submit
6) The predicate R(x,y) takes how many arguments?

Explanation

The predicate R(x,y) has two arguments: x and y. The number of arguments a predicate takes is called its arity, and it is fixed by the definition of the predicate. In this case, R is defined to take two arguments, so the arity is 2, regardless of the domain.
Submit
7) Which is NOT an open predicate?

Explanation

An open predicate is one that contains  variables and thus does not have a definite truth  value until the  variables are assigned  values. Options a, b, and d all contain  variables (x, y) and are therefore open. Option c, "5 is odd", is a statement about a specific constant (5) and has a definite truth  value (true), so it is a closed sentence / atomic formula with no free  variables.
Submit
8) Which formula is closed due to a quantifier?

Explanation

A closed formula is one that has no free  variables. In option c, the universal quantifier ∀x binds the  variable x in P(x), so there are no free  variables. Option a has free  variables x and y. Option b has a quantifier for x but y is still free. Option d has no  variables because a is a constant, so it is closed, but not by a quantifier.
Submit
9) Express “x is greater than y” using predicate symbol:

Explanation

In formal predicate notation, we use a predicate symbol (like G) to represent a relation. The relation "greater than" is typically represented by a predicate that takes two arguments in the order of the relation. So, "x is greater than y" is written as G(x,y). Option c is the opposite relation. Option a and b uses infix notation which is common in mathematics but not the formal predicate notation.
Submit
10) Domain of P(x): “x is an even integer”:

Explanation

The domain is the set of objects that the  variable x can take. The property "is an even integer" is defined for integers. While it could be applied to other numbers, the typical domain for this predicate is the set of integers because evenness is a property of integers.
Submit
11) Q(x): prime, R(x): x<10, Q(x) ∧ R(x) describes:

Explanation

The symbol ∧ stands for "and". So Q(x) ∧ R(x) means "x is prime and x is less than 10". This describes the set of numbers that are both prime and less than 10. It does not describe all prime numbers (because it requires x<10) nor all numbers less than 10 (because it requires primality).
Submit
12) N(x) is ¬P(x) where P(x): x>0. N(x) is:

Explanation

The negation of "x is positive" (which means x>0) is "x is not positive". This includes two cases: x is negative or x is zero. Therefore, the negation is "x ≤ 0". Option a only covers zero, option b only covers negative numbers, and option d is the original statement.
Submit
13) Truth value of G(Ada) if Ada studies logic:

Explanation

G(Ada) is a statement about a specific individual, Ada. Since we are told that Ada really studies logic, the statement "Ada studies logic" is true. Therefore, the truth  value is True.
Submit
14) In P(x): 'x is prime', P is:

Explanation

In the notation "P(x): x is a prime number", P is the predicate symbol that represents the property of being a prime number. It is not a specific number, not the truth  value (which would be true or false for a specific x), and not the domain (which is the set of objects x can be).

Submit
15) Which requires a logical connective?

Explanation

An atomic predicate is one that does not contain any logical connectives (like and, or, not). Options a, b, and d are atomic because they express a single property or relation. Option c contains the word "and", which is a logical connective, so it is a compound statement and requires the connective ∧ to be written formally.
Submit
×
Saved
Thank you for your feedback!
15)
Your input helps us improve, and you’ll get your detailed results next.
View My Results
Cancel
  • All
    All (15)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
Which of the following shows an application of a predicate symbol?
What does P(x) represent in predicate logic?
Which represents “x is greater than 5” using a predicate symbol?
Negation of P(x) in direct syntactic form:
“x does not satisfy P” is:
The predicate R(x,y) takes how many arguments?
Which is NOT an open predicate?
Which formula is closed due to a quantifier?
Express “x is greater than y” using predicate symbol:
Domain of P(x): “x is an even integer”:
Q(x): prime, R(x): x<10, Q(x) ∧ R(x) describes:
N(x) is ¬P(x) where P(x): x>0. N(x) is:
Truth value of G(Ada) if Ada studies logic:
In P(x): 'x is prime', P is:
Which requires a logical connective?
Alert!

Advertisement