Let A and B be two sets Show that the sets AxB and BxA have an element in common - Maths - Relations and Functions

Question

Let A and B be two sets Show that the sets AxB and BxA have an
element in common if the sets A and B have an element in common

Priyanka Kedia · Accepted Answer

Let A and B be two non empty sets having k elements in common
So,nA∩B=kNow, we know that,A∩B×B∩A=A×B∩B×ASo,nA×B∩B×A=nA∩B×B∩A                                =nA∩B×nB∩A                                =nA∩B×nA∩B                                =k×k                                =k2Thus, A×B and B×A have k2 elements in common

Let A and B be two sets. Show that the sets AxB and BxA have an element in common if the sets A and B have an element in common.