If n A -3- m B -4- then write n A - A - B -

We have, n(A) = 3, n(B) = 4 ∴ n (A × A × B) = n(A) × n(A × B) [∵ n(A × B) = n(A) × n(B)] = n(A) × n(A) × n(B) = 3 × 3 × 4 = 36 ⇒ n(A × A × B) = 36 ...

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Standard XII

Mathematics

Number of Elements in a Cartesian Product

If n A =3, m ...

Question

If n(A) = 3, m(B) = 4, then write $n (A \times A \times B) .$

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Solution

We have,

$n (A) = 3, n (B) = 4$

$∴ n (A \times A \times B) = n (A) \times n (A \times B)$

$[∵ n (A \times B) = n (A) \times n (B)]$

$= n (A) \times n (A) \times n (B)$

$= 3 \times 3 \times 4$

$= 36$

$\Rightarrow n (A \times A \times B) = 36$

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If n(A) = 3, m(B) = 4, then write n(A×A×B).

We have, n(A)=3,n(B)=4 ∴n(A×A×B)=n(A)×n(A×B) [∵n(A×B)=n(A)×n(B)] =n(A)×n(A)×n(B) =3×3×4 =36 ⇒n(A×A×B)=36

If n(A) = 3, m(B) = 4, then write $n (A \times A \times B) .$

We have,

$n (A) = 3, n (B) = 4$

$∴ n (A \times A \times B) = n (A) \times n (A \times B)$

$[∵ n (A \times B) = n (A) \times n (B)]$

$= n (A) \times n (A) \times n (B)$

$= 3 \times 3 \times 4$

$= 36$

$\Rightarrow n (A \times A \times B) = 36$