"If A = {x $\in$ R : |x $-$ 2| 1}, B = {x $\in$ R : $\sqrt {{x^2} - 3}$ 1}, C = {x $\in$ R : |x $-$ 4| $\ge$ 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 is ________________."

Question

"If A = {x $\in$ R : |x $-$ 2| > 1}, B = {x $\in$ R : $\sqrt {{x^2} - 3}$ > 1}, C = {x $\in$ R : |x $-$ 4| $\ge$ 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 is ________________."

Accepted Answer

"A = ($-$$\infty$, 1) $\cup$ (3, $\infty$)

B = ($-$$\infty$, $-$2) $\cup$ (2, $\infty$)

C = ($-$$\infty$, 2] $\cup$ [6, $\infty$)

So, A $\cap$ B $\cap$ C = ($-$$\infty$, $-$2) $\cup$ [6, $\infty$)

z $\cap$ (A $\cap$ B $\cap$ C)' = {$-$2, $-$1, 0, $-$1, 2, 3, 4, 5}

Hence, no. of its subsets = 2⁸ = 256."

If A = {x $\in$ R : |x $-$ 2| > 1},
B = {x $\in$ R : $\sqrt {{x^2} - 3}$ > 1},
C = {x $\in$ R : |x $-$ 4| $\ge$ 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 is ________________.

Solution

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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| $\ge$ 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 is ________________.

Solution

About this question

More Sets, Relations and Functions questions

Drill 25 more like these. Every day. Free.

If A = {x $\in$ R : |x $-$ 2| > 1},
B = {x $\in$ R : $\sqrt {{x^2} - 3}$ > 1},
C = {x $\in$ R : |x $-$ 4| $\ge$ 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 is ________________.