Let n(A) = 3 and n(B) = 3 (where n(S) denotes | vedclass

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

Question

(C) Given $n(A) = 3$ and $n(B) = 3$,the number of elements in the Cartesian product $A 	imes B$ is $n(A 	imes B) = n(A) 	imes n(B) = 3 	imes 3 = 9

Vedclass · Accepted Answer

$256$

Vedclass · Answer

(C) Given $n(A) = 3$ and $n(B) = 3$,the number of elements in the Cartesian product $A 	imes B$ is $n(A 	imes B) = n(A) 	imes n(B) = 3 	imes 3 = 9$.The number of subsets of a set with $m$ elements having an odd number of elements is given by the sum of combinations $\sum_{k 	ext{ is odd}} \binom{m}{k} = \binom{m}{1} + \binom{m}{3} + \dots + \binom{m}{m}$.For $m = 9$,this sum is $\binom{9}{1} + \binom{9}{3} + \binom{9}{5} + \binom{9}{7} + \binom{9}{9}$.Using the identity $\sum_{k 	ext{ is odd}} \binom{m}{k} = 2^{m-1}$,we get $2^{9-1} = 2^8 = 256$.

Let $n(A) = 3$ and $n(B) = 3$ (where $n(S)$ denotes the number of elements in set $S$). Then,the number of subsets of $(A \times B)$ having an odd number of elements is:

Similar Questions

If $R$ is the set of all real numbers,what do the Cartesian products $R \times R$ and $R \times R \times R$ represent?

Let $A, B, C$ be three sets such that $n(A \cap B) = n(B \cap C) = n(C \cap A) = n(A \cap B \cap C) = 2$. Then $n((A \times B) \cap (B \times C))$ is equal to -

If two sets $A$ and $B$ have $99$ elements in common,then the number of elements common to each of the sets $A \times B$ and $B \times A$ is

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

Let $A = \{1, 2\}$,$B = \{1, 2, 3, 4\}$,$C = \{5, 6\}$,and $D = \{5, 6, 7, 8\}$. Verify that $A \times C$ is a subset of $B \times D$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module