Question

Let A={a,b,c} and B={1,2,3,4,5}. Determine ​n(AxB​).
a) 5
b) 10
c) 12
d) 15

Answer 1

The number of elements in the Cartesian product of sets A and B, denoted as n(AxB), is calculated by multiplying the number of elements in set A with the number of elements in set B, resulting in 3 × 5 = 15.

Step-by-step explanation:

To determine n(AxB), we need to calculate the cardinality (the number of elements) of the Cartesian product of sets A and B. The set A contains 3 elements (a, b, c) and set B contains 5 elements (1, 2, 3, 4, 5). The Cartesian product AxB will consist of all possible ordered pairs where the first component is from set A and the second component is from set B.

The formula for the number of elements in the Cartesian product of two sets is:

n(A) × n(B)

So:

n(AxB) = n(A) × n(B) = 3 × 5 = 15

Therefore, the correct answer is (d) 15.