2.3 Sets and Venn Diagrams

What is the difference between disjoint sets and overlapping sets?

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

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

• Disjoint sets are subsets of overlapping sets; overlapping sets are not subsets of disjoint sets.

• Disjoint sets can be equal; overlapping sets cannot be equal.

What does the empty set represent?

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

• A set containing all possible elements.

• A set with one element only.

• A set that cannot be defined.

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.

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

• {1, 2, 5, 6}

• {3, 4}

• {1, 2, 3}

• {5, 6}

What does A' ∪ B represent?

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

• Elements that are in both A and B.

• Elements that are only in A.

• Elements that are neither in A nor in B.

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

• {1, 2, 3}

• {2, 3}

• {1, 2, 3, 4}

• {3, 4}

What is the complement of set A denoted as?

• A'

• A^c

• A*

• A~

What is a universal set?

• A set that contains all possible elements for a particular discussion.

• A set that contains no elements at all.

• A set that includes only prime numbers.

• A set that contains only even numbers.

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

• A ∪ B

• A - B

• A ∩ B

• A ⊕ B