Let X, Y, Z and W be sets defined on the universal set $U = N $ as follows: How can I solve this Venn Diagram?

Question

So I have the following assertions and I have to illustrate this on a Venn Diagram.

• $ (X - Y) \cap Z = ${1,2,3,4}

• $ Y = $ {5,6}

• $Z \cap Y = \emptyset $

• $ W \cap (X - Z) =$ {7,8}

• $ X \cap W \cap Z = $ {2,4}

So I did the following code on Python,

import matplotlib.pyplot as plt
from matplotlib_venn import venn3

v = venn3(subsets = (1,2,3,4,5,6,0,7,8,2,4), set_labels = ('X', 'Y', 'Z', 'W'))



plt.show() 

but it's not working because I need Four-Ellipse Venn Diagram to solve it. And I have to specify when two sets intersects and when I have the diference between them.

I'm very stuck and I'm not able to find the logic in this exercise anymore. Any tips on how to solve it? I also tried to draw Venn Diagram on paper but I also failed.

Answer 1

here is what i did. first I get a big paper and draw three regions, like shown at this link: https://commons.wikimedia.org/wiki/File:Intersection_of_3_circles_0.svg

these regions I label X, Z, W. I think it is better to wait to draw region Y, because it is not clear where to put it initially. Then I look at the bullets (the requirements) individually.

bullet 5 is easy to satisfy. Now look at bullet 3; introduce the final circle for region Y so that bullet 3 is happy.

Next is bullet 4. You have to put 7,8 somewhere. There are two possible places to put 7,8. Which one is correct?