If A - a-b-2- 3- B - a-3- c- C- 1- 3- c- then n A - B - A - C is

A = {a,b,2, 3}, B = {a,3, c}, C= {1, 3, c} (A × B) ∩ (A × C) = A × (B ∩ C) (B ∩ C)= {3,c} n((A × B) ∩ (A × C)) =n(A × (B ∩ C)) =n(A) × n(B ∩ C) =4×2 =8 ...

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Standard XIII

Mathematics

Number of Elements in a Cartesian Product

If A = a,b,2,...

Question

If $A = {a, b, 2, 3}, B = {a, 3, c},$ $C = {1, 3, c},$ then $n ((A \times B) \cap (A \times C))$ is

9

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8

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Solution

The correct option is C $8$
$A = {a, b, 2, 3}, B = {a, 3, c},$ $C = {1, 3, c}$

$(A \times B) \cap (A \times C) = A \times (B \cap C) (B \cap C) = {3, c}$

$n ((A \times B) \cap (A \times C)) = n (A \times (B \cap C)) = n (A) \times n (B \cap C) = 4 \times 2 = 8$

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If A={a,b,2,3},B={a,3,c}, C={1,3,c}, then n((A×B)∩(A×C)) is

The correct option is C 8A={a,b,2,3},B={a,3,c}, C={1,3,c} (A×B)∩(A×C)=A×(B∩C)(B∩C)={3,c} n((A×B)∩(A×C))=n(A×(B∩C))=n(A)×n(B∩C)=4×2=8

If $A = {a, b, 2, 3}, B = {a, 3, c},$ $C = {1, 3, c},$ then $n ((A \times B) \cap (A \times C))$ is

The correct option is C $8$
$A = {a, b, 2, 3}, B = {a, 3, c},$ $C = {1, 3, c}$

$(A \times B) \cap (A \times C) = A \times (B \cap C) (B \cap C) = {3, c}$

$n ((A \times B) \cap (A \times C)) = n (A \times (B \cap C)) = n (A) \times n (B \cap C) = 4 \times 2 = 8$