How many binary relations are there on a set S with 9 distinct element

1.	How many binary relations are there on a set S with 9 distinct elements?
Answer» $\displaystyle\huge\red{\underline{\underline{Solution}}}$ DEFINITION TO BE MEMORISED CARTESIAN PRODUCT OF SETS Let A & B be any TWO non empty sets. The Cartesian product of A and B is denoted by A × B and defined by : $\sf{A \times B = \{ \:(a,b) : a \in \: A \: , b \in \:B \}}$ BINARY RELATION Let A and B be any two non empty sets. A binary relation R between A and B is a subset of A × B NUMBER OF BINARY RELATIONS If A and B be any two non empty sets such that $\sf{ \: n(A) = p \: \: and \: \: n(B) = q \: }$ Then the number of binary relations between A & B $\sf{= {2}^{pq} }$ Using the same we can say that the number of binary relations on a SET containing n is $\sf{ = {2}^{ {n}^{2} } }$ TO DETERMINE The number of binary relations are there on a set S with 9 DISTINCT elements CALCULATION $\sf{Here \: \: n(S) = 9}$ Hence The number of binary relations the set S $\sf{ \: = {2}^{(9 \times 9)} \: }$ $\sf{ = {2}^{81} \: }$ ━━━━━━━━━━━━━━━━ LEARN MORE FROM BRAINLY Let A = {1,8,27,64,125} and B= {1,2,3,4,5,6} and R be the relation ‘is cube of 'from A to B then domain of R is brainly.in/question/21096862

How many binary relations are there on a set S with 9 distinct elements?

Answer»

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

DEFINITION TO BE MEMORISED

CARTESIAN PRODUCT OF SETS

Let A & B be any TWO non empty sets. The Cartesian product of A and B is denoted by A × B and defined by :