Table of Contents
How many relations are there on a set with N elements that are transitive?
There is no simple formula for this number (but see http://oeis.org/A006905 for the values for small n). The case n=2 is small enough that you can list out all 16 different relations and count the ones that are transitive.
What is the number of relations on a set?
A relation on a set A is a set of all the ordered pairs of the power set of set A. The power set of {a,b,c} will have 2^k (k=# of elements of set A), i.e. 2^3=8 elements of the power set of A (all the possible subsets of A). Therefore 64 relations can be defined in a set of three elements.
How many relations are there on a set with N elements that are reflexive and symmetric?
whether it is included in relation or not) So total number of Reflexive and symmetric Relations is 2n(n-1)/2 .
How many relations are there on a set with N elements that are Antisymmetric?
There are (n2 − n)/2 pairs for (ai,aj) such that i = j. There- fore, there exists 3(n2−n)/2 antisymmetric binary relations. Also, observe that any subset of the diagonal elements is also an antisymmetric relation. Therefore, the number of antisymmetric binary relations is 2n · 3(n2−n)/2.
How many transitive relations are there on a set with N elements if’n 3?
Counting transitive relations
| Elements | Any | Equivalence relation |
|---|---|---|
| 1 | 2 | 1 |
| 2 | 16 | 2 |
| 3 | 512 | 5 |
| 4 | 65,536 | 15 |
How many relations are there on a set with N elements if a set A has m elements and a set B has n elements How many relations are there from A to B?
Answer: If there are n elements in the set A and m elements in the set B, then there will be (nxm) elements in AxB . Accordingly, there will be 2^(nxm) subsets of AxB and therefore there can be defined 2^(nxm) relations from A to B .
How do you find the number of relations on a set with three elements?
A relation on set P is a subset of P×P. In this case, |P|=3 so |P×P|=9. Hence there are 29 subsets of P×P, and thus 29 relations on P.
How many relations are possible from a set A of M elements to another set B of N elements Why?
If there are n elements in the set A and m elements in the set B, then there will be (nxm) elements in AxB . Accordingly, there will be 2^(nxm) subsets of AxB and therefore there can be defined 2^(nxm) relations from A to B .
What is the total number of possible relations in a set?
A set X with n elements has n 2 ordered pairs of elements, each of which can be in relation or not. That’s why the total number of possible relations is 2 n 2.
How many (NxM) relations can be defined from a to B?
A subset of the Cartesian product (AxB)of two sets A, B is a relation from A to B . If there are n elements in the set A and m elements in the set B, then there will be (nxm) elements in AxB . Accordingly, there will be 2^ (nxm) subsets of AxB and therefore there can be defined 2^ (nxm) relations from A to B .
How many subsets of a binary relation are there?
Now, any subset of AXA will be a relation, as we know that with n elements, 2^n subsets are possible, So in this case, there are 2^4=16 total possible relations. A binary relation on a set A is a subset of the pairs A × A. If A has n elements, then A × A has n 2 pairs. The relation could include none, any, or all of those pairs.
What is the total number of symmetric relations on a set?
A Relation ‘R’ on Set A is said be Symmetric if xRy then yRx for every x, y ∈ A. or if (x, y) ∈ R, then (y, x) ∈ R for every x, y?A. Total number of symmetric relations is 2n (n+1)/2.