(A) Given $A = \{x : x^2 - 5x + 6 = 0\}$.Solving the quadratic equation $x^2 - 5x + 6 = 0$,we get $(x - 2)(x - 3) = 0$,so $A = \{2, 3\}$.Given $B = \{

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(A) Given $A = \{x : x^2 - 5x + 6 = 0\}$.Solving the quadratic equation $x^2 - 5x + 6 = 0$,we get $(x - 2)(x - 3) = 0$,so $A = \{2, 3\}$.Given $B = \{2, 4\}$ and $C = \{4, 5\}$.The intersection $B \cap C$ is the set of common elements,so $B \cap C = \{4\}$.Now,the Cartesian product $A \times (B \cap C) = \{2, 3\} \times \{4\}$.This results in the set of ordered pairs $\{(2, 4), (3, 4)\}$.

Class 11 Mathematics Relations and Functions Cartesian Products of Sets

Medium

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

A
$\{(2, 4), (3, 4)\}$
B
$\{(4, 2), (4, 3)\}$
C
$\{(2, 4), (3, 4), (4, 4)\}$
D
$\{(2, 2), (3, 3), (4, 4), (5, 5)\}$

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Class 11

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Relations and Functions

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Cartesian Products of Sets

If $P = \{a, b, c\}$ and $Q = \{r\}$,find the sets $P \times Q$ and $Q \times P$. Are these two products equal?

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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 $P \times Q = \{(m, n), (n, m)\}$.

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If $(1, 3), (2, 5)$ and $(3, 3)$ are three elements of $A \times B$ and the total number of elements in $A \times B$ is $6$,then the remaining elements of $A \times B$ are

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Let $A = \{1, 2, 3\}$,$B = \{3, 4\}$,and $C = \{4, 5, 6\}$. Find $(A \times B) \cap (A \times C)$.

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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:

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

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If $P = \{a, b, c\}$ and $Q = \{r\}$,find the sets $P \times Q$ and $Q \times P$. Are these two products equal?

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 $(1, 3), (2, 5)$ and $(3, 3)$ are three elements of $A \times B$ and the total number of elements in $A \times B$ is $6$,then the remaining elements of $A \times B$ are

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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 $P \times Q = \{(m, n), (n, m)\}$.