Question Number 114233 by Aina Samuel Temidayo last updated on 18/Sep/20

If two sets A and B are having 99  elements in common, then the  number of elements common to each  of the sets A×B and B×A is

Answered by 1549442205PVT last updated on 20/Sep/20

A={x_1 ,x_2 ,...,x_m ,c_1 ,c_2 ,...,c_(99) }  B={y_1 ,y_2 ,...,y_n ,c_1 ,c_2 ,...,c_(99) }  ⇒A×B and B×A haveF_(99) ^2  =99^2   =9801common elements because  the common elements are  {(c_i ,c_j )(1≤i,j≤99)}

Commented by1549442205PVT last updated on 18/Sep/20

Thank you .I corrected.You just need  instead of 99 by 4 and check

Commented byAina Samuel Temidayo last updated on 18/Sep/20

Not correct.

Commented by1549442205PVT last updated on 20/Sep/20

It is F_(99) ^2 .Note F_n ^k =n^k .Note that  Given two sets A={x_i }_(i=1) ^m ,B={y_j }_(j=1) ^n   Then A×B={(x_i ,y_j )∣1≤i≤m,1≤j≤n}  B×A={(y_i ,x_j )∣1≤i≤n,1≤j≤m}