If nA-4-nB-3 andnA- B- C - 24- then nCis equal to

Explanation for the correct option:Given that n(A)=4,n(B)=3 andn(A× B× C) = 24The set (A× B× C) is the cartesian product of the sets A,B,CThe number of element ...

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Byju's Answer

Standard XII

Mathematics

Definition of Sets

If nA=4,nB=3 ...

Question

If $n (A) = 4$ , $n (B) = 3$ and $n (A \times B \times C) = 24$ , then $n (C)$ is equal to

$288$

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$1$

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$17$

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$12$

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$2$

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Solution

The correct option is E
$2$

Explanation for the correct option:
Given that $n (A) = 4$ , $n (B) = 3$ and $n (A \times B \times C) = 24$
The set $(A \times B \times C)$ is the cartesian product of the sets $A, B, C$
The number of elements in the cartesian product are given as
$n (A \times B \times C) = n (A) \times n (B) \times n (C)$
Substituting the values we get
$\Rightarrow$ $24 = 4 \times 3 \times n (C)$
$\Rightarrow$ $n (C) = 2$
Thus the value of $n (C)$ is $2$ .
Hence, option(E) is the correct answer.

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If n(A)=4,n(B)=3 andn(A×B×C)=24, then n(C)is equal to

If $n (A) = 4$ , $n (B) = 3$ and $n (A \times B \times C) = 24$ , then $n (C)$ is equal to