(D) Given that $n(A) = 4$ and $n(B) = 3$. We know that for any finite sets $A$,$B$,and $C$,the number of elements in the Cartesian product is given by

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(D) Given that $n(A) = 4$ and $n(B) = 3$. We know that for any finite sets $A$,$B$,and $C$,the number of elements in the Cartesian product is given by $n(A \times B \times C) = n(A) \times n(B) \times n(C)$. Substituting the given values: $4 \times 3 \times n(C) = 24$ $12 \times n(C) = 24$ $n(C) = \frac{24}{12} = 2$. Thus,the correct option is $D$.

Class 11 Mathematics Set Theory Basic of Set theory

Easy

If $n(A) = 4$,$n(B) = 3$,and $n(A \times B \times C) = 24$,then find $n(C)$.

A
$288$
B
$1$
C
$12$
D
$2$

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Basic of Set theory

What universal set $(U)$ would you propose for each of the following:
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The set $A = \{ x : x \in \mathbb{R}, x^2 = 16 \text{ and } 2x = 6 \}$ is equal to

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The remainder obtained when the polynomial $1 + x + x^3 + x^9 + x^{27} + x^{81} + x^{243}$ is divided by $x - 1$ is

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If $n(A) = 3$ and $n(B) = 6$ and $A \subseteq B$,then the number of elements in $A \cap B$ is:

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If $n(A) = 4$,$n(B) = 3$,and $n(A \times B \times C) = 24$,then find $n(C)$.

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What universal set $(U)$ would you propose for each of the following:The set of isosceles triangles

Write the set $\{ \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7} \}$ in the set-builder form.

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What universal set $(U)$ would you propose for each of the following:
The set of isosceles triangles