Satish wishes to know the number of reflexive relations defined on the set . How many such relations are possible ?

Question

In two different societies, there are some school going students including girls as well as boys. Satish forms two sets with these students for his college project.

Let = {a₁, a₂, a₃, a₄, a₅ } and B= {b₁, b₂, b₃, b₄ } where ai's and bi's are school going students of first and second societies respectively.

Satish decides to explore these sets for various types of relations and functions.

With the help of above information answer the following question:

Satish wishes to know the number of reflexive relations defined on the set . How many such relations are possible ?

Answer 1

We know that total number of reflexive relations on set A having n element is 

2^{\(n^2-n\).}

 Given that = {a₁, a₂, a₃, a₄, a₅ }.

Therefore, A has 5 elements.

Therefore, total number of reflexive relations defined on the set A = 2^{\(5^2-5\)}. = 2²⁰.