If A - y - y -3 x - x - 2- x - N B - x - x is a positive even number- x -14 and C -1-4-8- then n A - B - A - C isA- 8B- 20 - 36D- 40

The correct option is A 8A = {y:|y|=3x, x≤2, x∈ℕ}, A={ 3, 6,3,6} B= {x:x is a positive even number, x lt;14} nbsp;B= {2, 4, 6, 8, 10, 12} and C = {1, 4, ...

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Byju's Answer

Standard XII

Mathematics

Number of Elements in a Cartesian Product

If A = y :| y...

Question

If $A = {y : | y | = 3 x, x \leq 2, x \in N},$
$B = {x : x is a positive even number, x < 14}$ and $C = {1, 4, 8},$ then $n ((A \times B) \cap (A \times C))$ is

40

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8

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20

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36

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Solution

The correct option is B $8$
$A = {y : | y | = 3 x, x \leq 2, x \in N}, A = {- 3, - 6, 3, 6} B = {x : x is a positive even number, x < 14} B = {2, 4, 6, 8, 10, 12}$ and $C = {1, 4, 8}$

$(A \times B) \cap (A \times C) = A \times (B \cap C)$

$B \cap C = {4, 8}$

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

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Similar questions

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If A={y:|y|=3x,x≤2,x∈N}, B={x:x is a positive even number,x<14} and C={1,4,8}, then n((A×B)∩(A×C)) is

The correct option is B 8A={y:|y|=3x,x≤2,x∈N},A={−3,−6,3,6}B={x:x is a positive even number,x<14}B={2,4,6,8,10,12} and C={1,4,8} (A×B)∩(A×C)=A×(B∩C) B∩C={4,8} ∴n((A×B)∩(A×C))=n(A×(B∩C))=n(A)×n(B∩C)=4×2=8

If $A = {y : | y | = 3 x, x \leq 2, x \in N},$
$B = {x : x is a positive even number, x < 14}$ and $C = {1, 4, 8},$ then $n ((A \times B) \cap (A \times C))$ is