If n(A)=4 and n(B)=2,then the number of subse | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given $n(A)=4$ and $n(B)=2$. The number of elements in the Cartesian product $A 	imes B$ is $n(A 	imes B) = n(A) 	imes n(B) = 4 	imes 2 = 8$.

Vedclass · Accepted Answer

$219$

Vedclass · Answer

(C) Given $n(A)=4$ and $n(B)=2$. The number of elements in the Cartesian product $A 	imes B$ is $n(A 	imes B) = n(A) 	imes n(B) = 4 	imes 2 = 8$. We need to find the number of subsets of $A 	imes B$ having at least $3$ elements. The total number of subsets of a set with $8$ elements is $2^8 = 256$. The number of subsets with $0, 1,$ or $2$ elements are given by $\binom{8}{0} + \binom{8}{1} + \binom{8}{2}$. $\binom{8}{0} = 1$,$\binom{8}{1} = 8$,and $\binom{8}{2} = \frac{8 	imes 7}{2} = 28$. Sum of these subsets $= 1 + 8 + 28 = 37$. The number of subsets with at least $3$ elements $= 2^8 - (\binom{8}{0} + \binom{8}{1} + \binom{8}{2}) = 256 - 37 = 219$.

If $n(A)=4$ and $n(B)=2$,then the number of subsets of the set $A \times B$ each having at least $3$ elements is:

Similar Questions

If $A = \{x : x^2 - 5x + 6 = 0\}, B = \{2, 4\}, C = \{4, 5\}$,then find $A \times (B \cap C)$.

State whether the following statement is true or false. If the statement is false,rewrite the given statement correctly.
If $P = \{m, n\}$ and $Q = \{n, m\}$,then $P \times Q = \{(m, n), (n, m)\}$.

If $A = \{ 2, 4, 5 \}$ and $B = \{ 7, 8, 9 \}$,then $n(A \times B)$ is equal to

If $A = \{1, 2, 3, 4\}$ and $B = \{a, b\}$,then the Cartesian product $A \times B$ is:

If $A, B$ and $C$ are any three sets,then $A \times (B \cup C)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module