Mathematical Logic and Set Theory Online Test

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Mathematical Logic and Set Theory

Description: Mathematical Logic and Set Theory Quiz
Number of Questions: 15
Created by: Aliensbrain Bot
Tags: mathematical logic set theory propositional logic predicate logic proofs

Which of the following is a tautology in propositional logic?

¬(P ∨ Q)
(P → Q) → ¬P
P ∨ (¬P ∧ Q)
¬(P ∧ Q) → (¬P ∨ ¬Q)

What is the negation of the statement "∀x ∈ R, x^2 ≥ 0"?

∃x ∈ R, x^2 < 0
∀x ∈ R, x^2 > 0
∃x ∈ R, x^2 ≤ 0
∀x ∈ R, x^2 ≠ 0

Which of the following is a valid inference rule in propositional logic?

Modus Ponens
Modus Tollens
Hypothetical Syllogism
Disjunctive Syllogism

What is the power set of the set {1, 2, 3}?

{{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}, ∅}
{{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
{{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}}
{{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}, ∅, {∅}}

Which of the following is an example of a bijection?

The function f: R → R defined by f(x) = x^2
The function g: R → R defined by g(x) = x + 1
The function h: R → R defined by h(x) = sin(x)
The function j: R → R defined by j(x) = |x|

What is the cardinality of the set of all subsets of the set {1, 2, 3}?

2^3
3^2
2^4
3^3

Which of the following is an example of a countable set?

The set of all natural numbers
The set of all rational numbers
The set of all real numbers
The set of all functions from R to R

What is the complement of the set {x ∈ R | x^2 < 4}?

{x ∈ R | x^2 ≥ 4}
{x ∈ R | x^2 > 4}
{x ∈ R | x^2 ≤ 4}
{x ∈ R | x^2 ≠ 4}

Which of the following is an example of a valid argument in first-order logic?

All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
All dogs are mammals. All mammals are animals. Therefore, all dogs are animals.
Some birds can fly. Tweety is a bird. Therefore, Tweety can fly.
No cats are dogs. Garfield is a cat. Therefore, Garfield is not a dog.

What is the negation of the statement "∃x ∈ R, x^2 = 2"?

∀x ∈ R, x^2 ≠ 2
∃x ∈ R, x^2 > 2
∀x ∈ R, x^2 < 2
∃x ∈ R, x^2 ≤ 2

Which of the following is an example of a deductive argument?

The sky is blue. Therefore, the grass is green.
All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
I saw a black cat yesterday. Therefore, all cats are black.
I like chocolate ice cream. Therefore, everyone likes chocolate ice cream.

What is the cardinality of the set of all functions from the set {1, 2, 3} to the set {a, b, c}?

3^3
3^2
2^3
2^2

Which of the following is an example of a non-constructive proof?

Proof by contradiction
Proof by mathematical induction
Proof by exhaustion
Proof by construction

What is the intersection of the sets {1, 2, 3} and {2, 3, 4}?

{1, 2, 3, 4}
{1, 2, 3}
{2, 3}
{1, 4}

Which of the following is an example of a countably infinite set?

The set of all natural numbers
The set of all rational numbers
The set of all real numbers
The set of all functions from R to R

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