Discussion Forum

Lat A and B be the two sets containing four and two elements respectively. Then, the number  of subsets of the  set A X B , each having at least three elements are,

Answer:

Explanation:

Given, n(A)=4,   n(B)=2

  $\Rightarrow$     n( A X B)= 8

   Total number of subsets of set

                       (A X B) =   $2^{8}$

Number of subsets of set A X B  hacing no element   (i.e, Φ)=1

 Number  od subsets of set A XB  having one element=   $^{8}C_{1}$

Number of subsets of set AX B  having two elements = $^{8}C_{2}$

$\therefore$       Number of subsets having atleast three elements

                             =   $2^{8}-(1+^{8}C_{1}+^{8}C_{2})$

                            =   $2^{8}-1-8-28$

                               =  $2^{8}-37$

                                  =256-37

                                 =219