- #1
MrWarlock616
- 160
- 3
Homework Statement
Show that if a set has 3 elements, then we can find 8 relations on A that all have the same symmetric closure.
Homework Equations
Symmetric closure ##R^* = R \cup R^{-1} ##
The Attempt at a Solution
If the symmetric closures of n relations are the same then we have,
## R_1 \cup R_1^{-1} = R_2 \cup R_2^{-1} = ... = R_n \cup R_n^{-1} ##
I have to prove n=8 for |A| = 3
Also, ##R_1##, ##R_2##,...,##R_n## can't be symmetric. A friend told me to use power sets but I don't see how that applies here.
Do I have to write down all possible relations that can occur from A={a,b,c} or is there a better way to prove this one?
Any help would be appreciated.
Last edited: