Free Practice Quiz Question List

8/9 8. Reasoning Errors and Informal Fallacies Online Quiz Questions

Use this free practice quiz with 20 questions to review 8/9 8. Reasoning Errors and Informal Fallacies, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

Which example is a valid counterexample to the claim “Every prime number is odd”?

A
3 is prime and odd.
B
2 is prime and not odd.
C
4 is not prime and even.
D
9 is not prime and odd.

Choose one

1 point

Which formula correctly formalizes “Some student passed,” assuming the domain contains all relevant objects?

A
$\exists x\,(Student(x)\land Passed(x))$
B
$\exists x\,(Student(x)\rightarrow Passed(x))$
C
$\forall x\,(Student(x)\land Passed(x))$
D
$\forall x\,(Student(x)\rightarrow Passed(x))$

Choose one

1 point

What does “Not all roads are open” mean?

A
Every road is closed.
B
No road is open.
C
At least one road is not open.
D
At least one road is open.

Choose all

1 point

Which two conditions must an object meet to serve as a valid counterexample to “All $A$ are $B$ ”? Select all that apply.

A
It belongs to the stated domain.
B
It supports the universal claim instead of contradicting it.
C
It satisfies the antecedent or class condition.
D
It is merely unrelated to the claim.

Choose all

1 point

Which two statements correctly describe what is needed to support an existential claim $\exists x\,P(x)$ ? Select all that apply.

A
It is an object in the domain.
B
It shows that every object has the property.
C
It satisfies the predicate.
D
It must be the only object with the property.

True or false

1 point

The truth value of a quantified statement can change when its domain of discourse changes.

A
True
B
False

True or false

1 point

The formulas $\forall x\,\exists y\,L(x,y)$ and $\exists y\,\forall x\,L(x,y)$ always express the same claim.

A
True
B
False

Written response

1 point

What is the logical term for one valid object that refutes a universal claim?

Written response

1 point

Write the symbolic negation of $\forall x\,P(x)$ .

Fill in the blank

1 point

The collection of objects over which a variable ranges is the , while the formula to which a quantifier applies is its .

Fill in the blank

1 point

To establish an existential claim, provide one valid : an object in the domain that satisfies the predicate.

Open ended

1 point

Formalize the negation of “Every student passed.” Explain in words what the negation asserts and why “No student passed” is too strong.

Choose one

1 point

Why is “For every customer, there is a representative” generally weaker than “There is one representative for every customer”?

A
They are equivalent because both mention every customer and a representative.
B
The first permits different representatives, while the second requires one representative for all customers.
C
The first requires one representative for all customers, while the second permits different representatives.
D
Neither statement makes a claim about representatives.

Choose one

1 point

Which formula correctly negates $\forall x\,[P(x)\rightarrow Q(x)]$ ?

A
$\forall x\,[\neg P(x)\lor Q(x)]$
B
$\exists x\,[\neg P(x)\rightarrow \neg Q(x)]$
C
$\exists x\,[P(x)\land \neg Q(x)]$
D
$\forall x\,[P(x)\land \neg Q(x)]$

Choose one

1 point

Which evaluation best explains the statement “Every real number has a reciprocal”?

A
The statement is true over all real numbers because every real number can be written as a fraction.
B
The statement is false over all real numbers but can be true over the nonzero real numbers.
C
The statement is false over every possible domain because zero is a real number.
D
The statement is true over all real numbers only when the domain includes integers.

True or false

1 point

True or false: From $\exists x\,P(x)$ , it follows that $\forall x\,P(x)$ .

A
True
B
False

Written response

1 point

What logical term names an object in the domain that satisfies a predicate and establishes an existential claim?

Choose one

1 point

Which statement best evaluates the reasoning “The claim worked for the first five cases, so it must be true for every case”?

A
Five examples always constitute a proof of a universal claim.
B
A universal claim is established whenever no counterexample has yet been found.
C
Testing examples proves a universal claim if the examples are chosen randomly.
D
Examples may suggest a pattern, but a proof or complete finite check is needed to establish the universal claim.

Choose one

1 point

Which argument most directly proves the universal claim that the sum of any two even integers is even?

A
The argument checks the first 100 pairs of even integers and finds that each sum is even.
B
The argument lets $m=2a$ and $n=2b$ be arbitrary even integers and derives $m+n=2(a+b)$ .
C
The argument gives one pair of even integers whose sum is even.
D
The argument assumes that because the claim sounds plausible, no counterexample exists.

Written response

1 point

Formalize the statement “Every student passed” in predicate logic, taking the overall domain to include all relevant objects and using $Student(x)$ and $Passed(x)$ as predicates.