##### Counting the Relations (3)

**4. Antisymmetric Relations:-**

Here Diagonal elements have 2 choices but

for non-diagonal pairs have three choices:

- 1
^{st }element of pair is present or - 2
^{nd}element of pair is present or - Both are absent.

let |A| =n then and R is a relation from A to A, so

Total number of elements in R = n^{2}

Total number of Diagonal pair = n

Total number of Non- Diagonal pair = and each have 3 choices

So Total number of **Antisymmetric Relations = **

**5. Asymmetric Relations:**

**Diagonal pairs **have only one choice as they are not allowed here.

Non-Diagonal pairs have three choices:

- 1
^{st }element of pair is present or - 2
^{nd}element of pair is present or - Both are absent.
- So total number of
**Asymmetric Relation**=