algebraic proof to show that for all sets X,Y and Z : (X – Y)n ZC = x – (Y U Z) Use an

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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3. Use an algebraic proof to show that for all sets X,Y and Z : (X – Y)n ZC = X – (Y U Z)
Do not justify each step. This should take less than six lines. Points will be given for clarity. Feel free
to work it out on scratch paper, but write up the final solution here.
Transcribed Image Text:3. Use an algebraic proof to show that for all sets X,Y and Z : (X – Y)n ZC = X – (Y U Z) Do not justify each step. This should take less than six lines. Points will be given for clarity. Feel free to work it out on scratch paper, but write up the final solution here.
Expert Solution
Step 1

Given sets X, Y, Z

To prove (X-Y)Zc=X-(YZ)

Step 2

Let x(X-Y)Zc

x(X-Y)   and   x  ZcxX   and   xY   or   x  Z

this implies 

xX   and   xY   or   x  ZxX   and   xY   Zx X - Y   Z

 

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