Respuesta :
We will assume A×B = B×A and show that A and B are necessarily the same.
Assume A×B = B×A. Let a ∈ A and b ∈ B. Then (a,b) ∈ A×B. Since A×B = B×A, we have (a,b) ∈ B×A. That is, a ∈ B and b ∈ A. Therefore, a ∈ A implies a ∈ B and b ∈ B implies b ∈ A. So A = B, as we had set out to do.
Assume A×B = B×A. Let a ∈ A and b ∈ B. Then (a,b) ∈ A×B. Since A×B = B×A, we have (a,b) ∈ B×A. That is, a ∈ B and b ∈ A. Therefore, a ∈ A implies a ∈ B and b ∈ B implies b ∈ A. So A = B, as we had set out to do.
Answer:
AXB={ (a, b) | a E A and b E B} where a is in A and b is in B
BXA={ (b, a) | b E B and a E A}
Since Cartesian product is a set of ordered pairs, ordering is important hence (a, b) does not equal to (b, a) unless a and b are equal
Step-by-step explanation:
