Given the following sets: Z = { z | z is an integer}W= { w | w is a whole number} (continued...)X = { x | x = 2z + 2, z is an element of Z} X is a subset of ZY = { b | b = 2z + 1, z is an element...

Given the following sets:

Z = { z | z is an integer}
W= { w | w is a whole number} (continued...)

X = { x | x = 2z + 2, z is an element of Z} X is a subset of Z
Y = { b | b = 2z + 1, z is an element of Z} Y is a subset of Z

Determine the following: (X union Y)-W

Explain your answer.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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Notice that the elements of the X subset are integer even numbers.

Take z=-1 => 2z+2 = -2+2 = 0

Take z=0 => 2z+2 = 2

Take z = 1 => 2z+2 = 4

................................

Notice that the elements of the Y subset are integer odd numbers.

Take z = -1 => 2z+1 = -1

Take z=0 => 2z+1 = 1

Take z = 1 => 2z+1 = 3

The union of X and Y subsets is a set containing the collection of all the elements of the X and Y subsets.

XUY = Z = W

Evaluating the difference XUY-W yields a set of elements that belong to XUY but they do not belong to W.

Since XUY = W => the result of difference is W or XUY. 

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