Question

plzzz help
Show that if A and B are two non-empty sets, having n elements in common then AXB anb BXA have n^2 elements in common.

Answer 1

IF N^2 elements be in common so should be A=B

Answer 2

cause of (x,y)=(y,x) then x=y

Answer 3

One sec still working on it

Answer 4

ha k thanx

Answer 5

brb getting tea

Answer 6

@zarkon I need more brains

Answer 7

\[\text{ If } |A \cap B|=1, \text{ then there is element } x \text{ such that } x \in A \cap B \]

\[(A \times B ) \cap( B \times A)=\{(x,x)\} => |A \cap B|=1=1^2\]

Answer 8

\[\text{ If } | A \cap B| =k , \text{ there there are elements} x_1,x_2,x_3,...x_k \in A \cap B \]

Answer 9

well
i can't put my opinion here cause i can't understand the question or i didn't study that Branch yet So lead the Ship @myininaya & i'm following u :)

Answer 10

\[(A \times B ) \cap (B \times A)= \{ (x_1,x_1), (x_1,x_2),(x_1,x_3),...(x_1,x_k),(x_2,x_1),...\]
\[(x_2,x_k),...(x_k,x_1),...(x_k,x_k) \}\]

Answer 11

Do you see that is k^2 elements
like we have all the k elements with (x_1,blah)
then we have k elements with (x_2,blah)
then k elements with (x_3,blah)
then ....
k elements with (x_k, blah)

Answer 12

you have k, k times