Question

Let A and B be two sets. Show that the sets A x B and Bx A have an element in common
the sets A and B have an element in common.​

Answer 1

Answer:

Proof:

Step-by-step explanation:

Let Set A= {1,2,3}

and Set B= {3,4}

In set A and set B, the common element is 3

A×B= { (1,3), (1,4),(2,3),(2,4),(3,3),(3,4)}

B×A= { (3,1),(3,2),(3,3),(4,1),(4,2),(4,,3)}

In sets A x B and Bx A, the common element is (3,3) which is also 3 and equal to the sets A and B have an element in common.

Hence proved.