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 freeto work it out on scratch paper, but write up the final solution here.

Name: 3. Use an algebraic proof to show that for all sets X,Y and Z : (X –
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Description: 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 freeto work it out on scratch paper, but write up the fin

Given sets X, Y, Z To prove (X-Y)∩Zc=X-(Y∪Z)

Answered: algebraic proof to show that for all…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.

Expert Solution

Step 1

Given sets $X, Y, Z$

To prove $(X - Y) \cap Z^{c} = X - (Y \cup Z)$

Step 2

Let $x \in (X - Y) \cap Z^{c}$

$x \in (X - Y) a n d x \in Z^{c} x \in X a n d x \notin Y o r x \notin Z$

this implies

$x \in X a n d (x \notin Y o r x \notin Z) x \in X a n d (x \notin Y \cup Z) x \in X - (Y \cup Z)$

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