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If A = ${x \in R; | x - 2 | > 1}, B = {x \in R : \sqrt[]{x^{2} - 3} > 1},$ $C = {x \in R; | x - 4 | \geq 2}$ and Z is the set of all integers, then the number of subsets of the set ${(A \cap B \cap C)}^{C} \cap Z i s$ ________

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Vishal Baghel | Contributor-Level 10

2 months ago

$| x - 2 | > 1 g i v e s x - 2 < - 1 o r x - 2 > 1$

i.e. x < 1 or x > 3 . (i) represent set A

$\sqrt[]{x^{2} - 3} > 1 g i v e s x^{2} - 3 > 1 o r x^{2} - 4 > 0$

x < 2 or x > 2 . (ii) represent set B

$| x - 4 | \geq 2 g i v e s x - 4 \leq - 2 o r x - 4 \geq 2$

$x \leq 2 o r x \geq 6$ . (iii)respect set C

so number of subset = 28 = 256

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If A = ${x \in R; | x - 2 | > 1}, B = {x \in R : \sqrt[]{x^{2} - 3} > 1},$ $C = {x \in R; | x - 4 | \geq 2}$ and Z is the set of all integers, then the number of subsets of the set ${(A \cap B \cap C)}^{C} \cap Z i s$ ________

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If A = { x ∈ R ; | x − 2 | > 1 } , B = { x ∈ R : x 2 − 3 > 1 } , C = { x ∈ R ; | x − 4 | ≥ 2 } and Z is the set of all integers, then the number of subsets of the set ( A ∩ B ∩ C ) C ∩ Z i s ________

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If A = ${x \in R; | x - 2 | > 1}, B = {x \in R : \sqrt[]{x^{2} - 3} > 1},$ $C = {x \in R; | x - 4 | \geq 2}$ and Z is the set of all integers, then the number of subsets of the set ${(A \cap B \cap C)}^{C} \cap Z i s$ ________