Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A imes B , each having atleast three elements are

Question

Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A 	imes B , each having atleast three elements are

Accepted Answer

Answer: A. 219 Given, \begin{aligned} &n(A)=4, n(B) =2 \\ &\Rightarrow n(A 	imes B) =8 \end{aligned} Total number of subsets of set (A 	imes B)=2^8 Number of subsets of set A 	imes B having no element (i.e. \phi)=1 Number of subsets of set A 	imes B having one element ={ }^8 C_1 Number of subsets of set A 	imes B having two elements ={ }^8 C_2 	herefore Number of subsets having atleast three elements \begin{aligned} &=2^8-\left(1+{ }^8 C_1+{ }^8 C_2ight) \\ &=2^8-1-8-28 \\ &=2^8-37 \\ &=256-37=219 \end{aligned}

Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A $\times$ B , each having atleast three elements are

Answer

Explanation

More JEE Math questions