Logic and Set Theory Quiz

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.

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)

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)

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)

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.

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))

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

• {∅}

• {0}

• ∅

• (0)

What is the cardinality of the set A = {x | x is a vowel in the English alphabet}?

• 3

• 4

• 5

• 6

What does A ∩ B represent?

• Union of A and B

• Elements unique to A

• Common elements of A and B

• Complement of A

If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ B?

• {3}

• {1, 2, 3, 4, 5}

• {1, 2, 3}

• {4, 5}