Question

if S and T have N elements in common.
Show that S×T and T×S have n2 elements in common.​

Answer 1

Answer:

The answer is in the attachment.

Answer 2

Let S and T have n elements in common.

Then:

(S X T) ∩ (U X V) = (S ∩ U) X (T ∩ V)

It is given that n(S∩T)=n elements

Now n[(S∩T)×(T∩S)]=n.n= $n^{2}$ elements

Hence proved.