01
Choose one
1 point
Consider the implication: “If a file is encrypted, then unauthorized users cannot read it.” In which situation is this implication false?
Free Practice Quiz Question List
08 — Discrete Mathematics for Computer Science Online Quiz Questions
Use this free practice quiz with 20 questions to review 08 — Discrete Mathematics for Computer Science, test your knowledge, and prepare for your next test or exam.
20 questions
02
Choose one
1 point
Suppose the following premises are true: “If file F is encrypted, unauthorized users cannot read F” and “File F is encrypted.” What conclusion follows by modus ponens?
- A
F is not encrypted.
- B
Unauthorized users can read F.
- C
Unauthorized users cannot read F.
- D
F is readable by everyone.
03
Choose one
1 point
Let A = {1, 2, 3}, B = {3, 4}, and C = {2, 4, 6}. What is (A ∪ B) ∩ C?
- A
{1}
- B
{2, 3}
- C
{2, 4}
- D
{1, 2, 3, 4, 6}
04
Written response
1 point
In the implication “If a program state is valid, then the next state satisfies the invariant,” what is the logical term for the condition “a program state is valid”?
05
Written response
1 point
A set A has exactly 4 elements. What is the number of elements in its power set 𝒫(A)?
06
Fill in the blank
1 point
Complete the two blanks: The negation of “for every x, P(x)” is “.” Therefore, “not every input is valid” means “.”
07
Choose one
1 point
For f: ℤ → ℤ defined by f(n) = n + 1, which classification is correct?
- A
f is bijective.
- B
f is injective but not surjective.
- C
f is surjective but not injective.
- D
f is neither injective nor surjective.
08
Choose all
1 point
Select all properties that a relation must have to be an equivalence relation on a set.
- A
For every a, aRa.
- B
If aRb, then bRa.
- C
If aRb and bRa, then a = b.
- D
If aRb and bRc, then aRc.
09
True or false
1 point
The function g: ℤ → ℤ defined by g(n) = n² is neither injective nor surjective.
- A
True
- B
False
10
Choose all
1 point
Select all steps or assumptions that belong to a standard proof by mathematical induction.
- A
Prove the statement for the first required value, such as 0.
- B
Assume the statement for an arbitrary k in the domain.
- C
Use the assumption to prove the statement for k + 1.
- D
Assume the statement is already true for every natural number.
11
Fill in the blank
1 point
Let f(x) = x + 2 and g(x) = 2x + 1. Complete the calculation: (g ∘ f)(3) = .
12
Choose one
1 point
Which statement is a counterexample-based disproof of the claim “Every prime number is odd”?
- A
Every prime number greater than 2 is odd.
- B
2 is prime but not odd.
- C
Every even number is prime.
- D
Every odd number is prime.
13
Open ended
1 point
Prove the set identity A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) using the method of proving both inclusions.
14
Choose one
1 point
Under which assignment of truth values is the implication P → Q false?
- A
P is false and Q is true.
- B
P is true and Q is false.
- C
P is false and Q is false.
- D
P is true and Q is true.
15
True or false
1 point
True or false: The statement “Not every input is valid” is logically equivalent to “There exists an invalid input.”
- A
True
- B
False
16
Written response
1 point
Let A = {1, 2, 3} and B = {x, y}. What is the cardinality of A × B? Enter the exact whole-number value.
17
Choose one
1 point
Which formula expresses the statement “Every user has at least one password,” where u ranges over users, p ranges over passwords, and Has(u,p) means that user u has password p?
- A
∃p ∀u Has(u,p)
- B
∀p ∃u Has(u,p)
- C
∀u ∃p Has(u,p)
- D
∃u ∀p Has(u,p)
18
Choose one
1 point
On the integers, define a relation by a R b if and only if a and b have the same remainder when divided by 3. How should this relation be classified?
- A
It is only reflexive.
- B
It is a partial order but not an equivalence relation.
- C
It is symmetric and transitive but not reflexive.
- D
It is an equivalence relation.
19
Written response
1 point
What is the standard name of the rule of inference that derives ¬P from the premises ¬Q and P → Q? Enter the rule's standard name.
20
True or false
1 point
True or false: To prove that an implication P → Q is valid, it is logically sufficient to prove its contrapositive ¬Q → ¬P.
- A
True
- B
False