##### Couting the Relations

let A and B are set such that |A| =n and |B| = m

then |A*B| = m*n

**Relation: **It is a subset of cartesian product.

Since already we know |A*B| = m*n and each element in the cartesian product have two choices: either they want to be the part of the relation of they don't want.

2 choices for m*n elements so total no. relations possible = **2 ^{m*n}**

we have already discussed the types of relations. So let's know some more details:

**1. Number of Reflexive relations:-**

let |A| = n

Reflexive relations are always defined on the same set :

|A*A| = n^{2}

if there are n elements in the set then there will be n reflexive pairs like (1,1), (2,2) ... (n,n)

So all these pairs must be present in reflexive pairs so out of n^{2} elements n has one choice as they must be the part of relation but remaining n^{2} -n has two choice

**So total number of reflexive relations=**

**2. The number of Ir-Reflexive relations:**

Again those reflexive pairs have only one choice they must not be present so: one choice for 'n' elements and two choices for n^{2} -n elements.

**total number of Ir- reflexive relations=**

https://www.techtud.com/example-tbd/choose-correct-statement