Quiz on Set Theory

What is a set?

• A collection of objects

• A single object

• An empty collection

• A number

When are sets A and B equal?

• If they contain the same elements

• If they have the same number of elements

• If one is a subset of the other

• If they are both empty

What is the cardinality of a set with 3 distinct elements?

• 3

• 0

• Infinite

• 1

What is the power set of A = {x, y, z}?

• {∅, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}

• {x, y, z}

• {x, y}

• {∅}

What is the Cartesian product of A = {x, y} and B = {a, b, c}?

• {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c)}

• {(x, a), (y, a)}

• {(x, b), (y, b)}

• {(x, c), (y, c)}

What is the union of sets A and B?

• A ∪ B = {x | x ∈ A ∨ x ∈ B}

• A ∩ B = {x | x ∈ A ∧ x ∈ B}

• A - B = {x | x ∈ A ∧ x ∉ B}

• A^c = U - A

What does it mean for two sets to be disjoint?

• Their intersection is empty

• They are equal

• One is a subset of the other

• They have at least one element in common

What is the complement of a set A?

• U - A

• A ∪ B

• A ∩ B

• A - B

What is a proper subset?

• A ⊂ B if A is a subset of B and A ≠ B

• A ⊆ B if A is a subset of B

• A = B

• A ∩ B = ∅

What is the definition of a finite set?

• A set with a finite number of distinct elements

• A set with infinite elements

• A set with no elements

• A set with at least one element