Let A = {1, 2, 3, 4, 5} and B = {2, 3, 6, 7}. | vedclass

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

Question

(C) The Cartesian product of two sets $A$ and $B$ is defined as $A 	imes B = \{(a, b) : a \in A, b \in B\}$.For the intersection $(A 	imes B) \cap (

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) The Cartesian product of two sets $A$ and $B$ is defined as $A 	imes B = \{(a, b) : a \in A, b \in B\}$.For the intersection $(A 	imes B) \cap (B 	imes A)$,an element $(x, y)$ must satisfy $(x, y) \in A 	imes B$ and $(x, y) \in B 	imes A$.This implies $x \in A, y \in B$ and $x \in B, y \in A$.Therefore,$x \in (A \cap B)$ and $y \in (A \cap B)$.Given $A = \{1, 2, 3, 4, 5\}$ and $B = \{2, 3, 6, 7\}$,the intersection is $A \cap B = \{2, 3\}$.The number of elements in $A \cap B$ is $n(A \cap B) = 2$.The number of elements in $(A 	imes B) \cap (B 	imes A)$ is given by $n(A \cap B) 	imes n(A \cap B) = 2 	imes 2 = 4$.

Let $A = \{1, 2, 3, 4, 5\}$ and $B = \{2, 3, 6, 7\}$. Then the number of elements in $(A \times B) \cap (B \times A)$ is

Similar Questions

Out of $100$ families in the neighbourhood,$50$ have radios,$75$ have $TVs$ and $25$ have $VCRs$. Only $10$ families have all three and each $VCR$ owner also has a $TV$. If some families have radio only,how many have only $TV$?

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

The domain of the function $\sqrt{\log(x^2 - 6x + 6)}$ is

Range of the function $f(x) = 9 - 7\sin x$ is

The largest possible set of real numbers which can be the domain of $f(x) = \sqrt {1 - \frac{1}{x}} $ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module