Question

Let A = {1, 2, 3, 4), B = {4, 5, 6), and C= {6, 7). Find:

a.n(AUB)
b. n(BUC)
C. n(AUBUC)
d. n(A-B)
e. n(B-C)
f. n(A-C)

Answer 1

Let's find the cardinalities (number of elements) for the given sets and their unions and differences:

A = {1, 2, 3, 4}

B = {4, 5, 6}

C = {6, 7}

a. n(A ∪ B) - The cardinality of the union of A and B:

A ∪ B = {1, 2, 3, 4, 5, 6}

n(A ∪ B) = 6

b. n(B ∪ C) - The cardinality of the union of B and C:

B ∪ C = {4, 5, 6, 7}

n(B ∪ C) = 4

c. n(A ∪ B ∪ C) - The cardinality of the union of A, B, and C:

A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7}

n(A ∪ B ∪ C) = 7

d. n(A - B) - The cardinality of the set difference A - B:

A - B = {1, 2, 3}

n(A - B) = 3

e. n(B - C) - The cardinality of the set difference B - C:

B - C = {4, 5}

n(B - C) = 2

f. n(A - C) - The cardinality of the set difference A - C:

A - C = {1, 2, 3, 4}

n(A - C) = 4

So, the cardinalities of the requested sets are:

a. n(A ∪ B) = 6

b. n(B ∪ C) = 4

c. n(A ∪ B ∪ C) = 7

d. n(A - B) = 3

e. n(B - C) = 2

f. n(A - C) = 4