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 intersection Y

Explain your answer.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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The intersection of the subsets X and Y is the void set or empty set. The elements of subset X are even numbers: x=2z+2 and the elements of the subset Y are odd numbers: b=2z+1.

The even elements of X are:

X={...2(-z)+2,...,-4,-2,0,2,4,...,2z+2,...}

The odd elements of Y subset are:

Y={...,2(-z)+1,...,-3,-1,1,3,....,2z+1,...}

You can see that the subsets X and Y have no common elements and the intersection of two sets must contain the common elements.

Answer: The intersection of X and Y is the empty set.

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