How many antisymmetrical relations are there on Set $B$ if Set $B = \{1,2,3\}$?
I believe its three?
Asked
Active
Viewed 199 times
1
-
2What is your reasoning for thinking it is three? – M47145 Apr 21 '16 at 19:06
-
Since pairs (1,1), (2,2) and (3,3) are relations? – Jay Apr 21 '16 at 19:09
-
5http://math.stackexchange.com/questions/503979/how-to-find-the-number-of-anti-symmetric-relations – peter.petrov Apr 21 '16 at 19:19
1 Answers
1
It's not so simple. Lookup the definitions again.
The set $S = B \times B$ has $9$ elements.
So the subsets of $S$ are $2^9$.
Each such subset is a relation on $B$.
Try to calculate how many subsets of $S$ do not contain both
$(a,b)$ and $(b,a)$ for any $a \neq b$. This is the count you are looking for.
peter.petrov
- 12,568