Question

Consider sets A = {1, 7, 3, a, b} and B = {1, 3, c}. Determine:

(a) n(A x B)
a. 10
b. 15
c. 12
d. 18

(b) n(B x B x B)
a. 27
b. 64
c. 125
d. 216

Answer 1

The cardinality of A x B is 15, and the cardinality of B x B x B is 27.

Step-by-step explanation:

The student is asking about cardinality of the Cartesian products of sets A = {1, 7, 3, a, b} and B = {1, 3, c}. The Cartesian product of two sets A and B, denoted as A x B, consists of all possible ordered pairs where the first element is from set A and the second element is from set B.

For part (a), we need to determine the cardinality of the Cartesian product A x B (denoted as n(A x B)). Set A has 5 elements and set B has 3 elements. The cardinality of the Cartesian product will be the product of the cardinalities of sets A and B which is 5 x 3 = 15.

For part (b), we need to find the number of elements in B x B x B. Since set B has 3 elements, the Cartesian product B x B x B will have 3 x 3 x 3 = 27 elements as it forms all possible ordered triples where each element is from set B.