# Thread: this i need guidance on this... please use these rules with a similar example

1. ## this i need guidance on this... please use these rules with a similar example

use the law of algebra of sets to that $

((X \cup Y) \cap (X \cup Y')) \cap ((X' \cup Y) \cap (X' \cup Y')) \;=\;\emptyset
$
please specify which rules you use in the derivation....

the laws i've been given for set operations are.....
idempotent laws
associative laws
commutative laws
distributive laws
identity laws
Involution laws
involution laws
complement laws
de morgans laws

2. Originally Posted by npm1
use the law of algebra of sets to that $

((X \cup Y) \cap (X \cup Y')) \cap ((X' \cup Y) \cap (X' \cup Y')) \;=\;\emptyset
$
please specify which rules you use in the derivation....

the laws i've been given for set operations are.....
idempotent laws
associative laws
commutative laws
distributive laws
identity laws
Involution laws
involution laws
complement laws
de morgans laws

Suppose $x\in \left(X\cup Y\right)\cap \left(X\cup Y'\right)$ and show that it must be that $x\in X$ ...now do the same for the other part of the right side of your expression (which is

almost the same as the left one but with $X'$ instead of $X$) , and show that it must be that $x\in X'$ ...deduce finally that the whole thing must be the empty set.

Tonio