Set Theory

Front

What is a proper subset?

Back

A proper subset of a set P is a subset that contains some but not all elements of P.

Front

How many proper subsets does a set with n elements have?

Back

A set with n elements has 2^n - 1 proper subsets.

Front

What does the symbol A ∩ B represent?

Back

A ∩ B represents the intersection of sets A and B, which includes all elements that are in both A and B.

Front

What does the symbol B' represent?

Back

B' represents the complement of set B, which includes all elements not in B.

Front

How do you calculate the number of students playing only one sport given overlapping sets?

Back

Use the principle of inclusion-exclusion to find the number of students in each category.

Front

What is the principle of inclusion-exclusion?

Back

The principle of inclusion-exclusion is a formula used to calculate the size of the union of multiple sets by including the sizes of the individual sets and excluding the sizes of their intersections.

Front

What does the symbol (G ∩ H)^c represent?

Back

(G ∩ H)^c represents the complement of the intersection of sets G and H, which includes all elements not in the intersection.

Front

What is the union of two sets?

Back

The union of two sets A and B, denoted A ∪ B, is the set of elements that are in A, in B, or in both.

Front

How do you find the intersection of multiple sets?

Back

The intersection of multiple sets includes only the elements that are present in all of the sets.

Front

What is the union of sets P and Q if P = {0, 1, 2, 3, 4} and Q = {4, 5, 6, 7}?

Back

The union P ∪ Q is {0, 1, 2, 3, 4, 5, 6, 7}.