Question

Prove the following : (a) If |A1| = n1, |A2|= n2 and |A3|= n3 then |A1 x A2 x A3| = n1n2n3

Answer 1

Consider and . With an element , we can form pairs: . The same number of pairs can be made with an element or with an element and with any other of the elements of the set . Those, it’s possible form of pairs in which the first element is selected from the set , and the second from the set . Further, from each pair and elements of set it is possible to obtain triples . Since we have pairs, then we will have triples of type as
elements of the , which we were must to prove.