Question

how many elements in A×B and B×A are common if n elements are common to A and B???​

Answer 1

Answer:

n × n = n² elements  are common in A×B and B×A

Step-by-step explanation:

If set A and set B have n element common then

A×B and B×A have to precisely those elements in common which are present in both

And

you know according to the definition of A×B

A×B = {(a,b) ║a ∈A ∧ b ∈ B}

Similarly

B×A = {(b,a) ║a ∈A ∧ b ∈ B}

And if n element are common in the A and B then

For some element in A×B and B×A

( a , b) = (b , a)

And

So

n × n = n² elements  are common in A×B and B×A