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Logic and Set Theory Quiz

Authored by Mary Quioc

Education

University

Used 1+ times

Logic and Set Theory Quiz
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35 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the statement ∃x ∃y (Reads(x, y) ∧ Book(y)) mean?

Everyone reads every book.

There is someone who reads at least one book.

All books are read by someone.

No one reads any book.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the negation of the statement ∀x ∀y Studies(x, y)?

∃x ∃y ¬Studies(x, y)

∃x ∀y ¬Studies(x, y)

∃y ∀x ¬Studies(x, y)

∃x ∃y Studies(x, y)

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Translate: 'There exists a teacher who teaches all subjects.'

∃x ∀y Teaches(x, y)

∃y ∀x Teaches(x, y)

∀x ∃y Teaches(x, y)

∃x ∃y Teaches(x, y)

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Translate to logic: 'Every researcher cites at least one article.'

∃x ∃y (Researcher(x) ∧ Article(y) ∧ Cites(x, y))

∀x (Researcher(x) → ∃y (Article(y) ∧ Cites(x, y)))

∃x ∀y (Researcher(x) ∧ Cites(x, y))

∀x ∃y Cites(x, y)

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which best describes ∃x ∀y (Has(x, y))?

Everyone has something.

There is someone who has everything.

Something is had by someone.

Everyone shares something.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the proper translation of 'Every parent loves their child'?

∀x ∃y (Parent(x, y) → Loves(x, y))

∃x ∀y (Parent(x, y) → Loves(x, y))

∀x ∀y (Parent(x, y) → Loves(x, y))

∃x ∃y (Parent(x, y) ∧ Loves(x, y))

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following is the correct representation of an empty set?

{∅}

{0}

(0)

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