2.3 Sets and Venn Diagrams

What is the difference between disjoint sets and overlapping sets?

• Disjoint sets have no elements in common; overlapping sets share some elements.

• Disjoint sets are subsets of overlapping sets.

• Overlapping sets are always larger than disjoint sets.

• Disjoint sets can have some elements in common.

What does the empty set represent?

• A set with no elements, denoted as {} or ∅.

• A set containing all possible elements.

• A set that contains at least one element.

• A set that is infinite.

If A = {1, 2, 3} and B = {4, 5, 6}, what is A ∩ B?

• ∅ (empty set)

• {1, 2, 3}

• {4, 5, 6}

• {1, 2, 3, 4, 5, 6}

What does A' ∪ B represent?

• Elements that are either not in A or in B.

• Elements that are only in A.

• Elements that are in both A and B.

• Elements that are not in A and also not in B.

What is the union of two sets A and B denoted as?

• A ∩ B

• A - B

• A ∪ B

• A × B

If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?

• {2}

• {2, 4}

• {3}

• {1, 2, 3}

What is the principle of inclusion-exclusion?

• A formula to calculate the size of the union of two sets: |A ∪ B| = |A| + |B| - |A ∩ B|.

• A method to find the intersection of multiple sets without overlap.

• A technique used to simplify complex mathematical expressions.

• A rule for determining the probability of independent events.

What is the shaded area representing A' ∩ B?

• Elements in A that are not in B.

• Elements in B that are not in A.

• Elements in both A and B.

• Elements that are neither in A nor in B.

What is the intersection of two sets A and B denoted as?

• A ∪ B

• A - B

• A ∩ B

• A ⊕ B

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

• {1, 2}

• {2, 3}

• {3, 4}

• {1, 4}