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# showing sets are equal watch

1. How to prove the following are equal? By the use of a combination of truth and membership table.

X` (Y Z) and (X` Y) Z

if (X` Y) ⊆ Z

The problem im having with this question is im not sure what to do with the third group of sets that contains the subset? if the question was to compare just 2 things i would be ok how does the third one come into it?

Also what is the proper name of e.g. X` (Y Z) Do i say "group of sets" or "relation of sets" etc
2. (Original post by andrewk)
How to prove the following are equal? By the use of a combination of truth and membership table.

X` (Y Z) and (X` Y) Z

if (X` Y) ⊆ Z

The problem im having with this question is im not sure what to do with the third group of sets that contains the subset? if the question was to compare just 2 things i would be ok how does the third one come into it?
It tells you, for example, that , and that , because there are no elements in that lie outside Z.

(Original post by andrewk)
Also what is the proper name of e.g. X` (Y Z) Do i say "group of sets" or "relation of sets" etc
Set. Specifically, it's an intersection of sets, namely an intersection of and , the latter of which is a union of sets (Y and Z). But the result is just another set. It's certainly not a group or a relation, both of which have other technical meanings.

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Updated: November 15, 2008
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