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 of Z} Y is a subset of Z Determine the following: (X union Y)’ Explain your answer.

Expert Answers

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Analyzing the elements in X it follows that they are even integer numbers. 

Any of the terms of X may be found using the formula x = 2z + 2, z in Z.

The pattern 2z + 2 is specific to the even numbers.

You may verify this statement plugging integer values instead of z in the relation x = 2z+2.

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

z = 0 => x = 2

z = 1 => x = 2+2 = 4

Notice that the results are integer even numbers.

Analyzing the elements in Y it follows that they are odd integer numbers. 

The union of X and Y is a set that collects elements from X or elements from Y. This collection of odd and even integer numbers represents the integer set Z.

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