Question

If A = (1,3,5) and B = (2,3) then find A × B and B × A

A)
A × B = ((1,2), (3,2), (5,2), (1,3), (3,3), (5,3))
B × A = ((1,2), (1,3), (3,2), (3,3), (5,2), (5,3))
B)
A × B = ((2,1), (2,3), (2,5), (3,1), (3,3), (3,5))
B × A = ((1,2), (1,3), (3,2), (3,3), (5,2), (5,3))
C)
A × B = ((1,2), (1,3), (3,2), (3,3), (5,2), (5,3))
B × A = ((2,1), (2,3), (2,5), (3,1), (3,3), (3,5))
D)
A × B = ((1,2), (3,2), (5,2), (1,3), (3,3), (5,3))
B × A = ((2,1), (3,1), (2,3), (3,3), (2,5), (3,5))

Answer 1

The Cartesian product A × B and B × A result in two different sets of ordered pairs. Option C is correct, with A × B =((1,2), (1,3), (3,2), (3,3), (5,2), (5,3)) and B × A = ((2,1), (2,3), (2,5), (3,1), (3,3), (3,5)).

Step-by-step explanation:

The question requires us to find the Cartesian product of two sets A and B, where A = (1,3,5) and B = (2,3). The Cartesian product A × B is a set of ordered pairs, each consisting of an element from A and an element from B. This means we pair every element from the first set with every element of the second set.

The Cartesian product A × B will look like this: A × B = ((1,2), (1,3), (3,2), (3,3), (5,2), (5,3)). For B × A, we pair each element from B with every element from A, resulting in B × A = ((2,1), (2,3), (2,5), (3,1), (3,3), (3,5)). Notice that in the Cartesian product, the order of the elements matters, hence A × B is different from B × A.

The answer is option C: A × B = ((1,2), (1,3), (3,2), (3,3), (5,2), (5,3)) and B × A = ((2,1), (2,3), (2,5), (3,1), (3,3), (3,5)).