Question

Let{5,6}how many binary operation can be defined on this set

Answer 1

Hello Friend

Here is your answer

Given that
{5,6}
Let the set be denoted by A

A = { 5,6}

Since A has two elements

=> A × A = 2 × 2 = 4 elements

A binary operation on A is function of A × A

Total Number of Binary Operation can be calculated by following formula


{n(A)}^n(A×A)

2^4 = 16

Hence the total No. Of Binary Operation is 16 on {5 ,6 }


Hope it helps
Jerri

Answer 2

$\bold{ans : 16}$

Let A = {5, 6}
you can see that A has two elements e.g., 5 and 6 .
then, number of elements in A × A = 2 × 2 = 4 elements

as you know, A binary operation on A is a function from A × A into A .
$e.g., \text{Total number of binary operation on A} = \bold{n(A)}^{n(A\times A)}$
here , n(A) means number of elements in set A
so, n(A) = 2
n(A × A) means number of set in A × A
so, n(A × A) = 4

now, number of binary operation on {5,6} = 2⁴ = 16 .