Suppose the sample space is S = {x| - 8 <= x <= 8}. Let A...

Suppose the sample space is S = {x| - 8 <= x <= 8}. Let A = {x|-2 < x < 2}, B = {x| -3 < x < -1}, and C = {x|1<x<3}. Determine the sets (A intersection B intersection C')'.

Please show work as needed.

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Expert Solution

Intersection : The intersection of sets A, B and C is the set of elements that are common to sets A, B and C. It is denoted by A ∩ B ∩ C.

Here, Sample space S = {x| - 8 <= x <= 8} i.e S= {-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8},

A = {x|-2 < x < 2} i.e. A={-1,0,1}, B = {x| -3 < x < -1} i.e. B ={-2} and C = {x|1<x<3} i.e. C = {2}

C' = the set of all elements in the sample space that are not in C = S - C = {-8,-7,-6,-5,-4,-3,-2,-1,0,1,3,4,5,6,7,8}

The set (A intersection B intersection C')' = includes the elements which are not in set (A intersection B intersection C') and the set (A intersection B intersection C') includes the values common in set A , set B and Set C'.

Hence, set (A intersection B intersection C') = = {} , since no elements is common in

set A , set B and Set C'.

Therefore, (A intersection B intersection C')' = = = {-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8}

i.e (A intersection B intersection C')' = = {x| - 8 <= x <= 8}.

orchestra answered 1 year ago

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