Question

Let A ={5,6}; how many binary operations can be defined on this set

Answer 1

$\bold{\large{A}}$ = {5,6} has two elements e.g., 5 and 6 as you can see.
e.g., n(A) = 2 [ n(A) shows number of elements in set A }
Then, $\bold{\large{A}}\times\bold{\large{A}}$ has 2 × 2 = 4 elements .
e.g., n(A × A) = 4

we know,
number of binary operation on set A=$\bold{n(A)}^{n(\bold{\large{A}}\times\bold{\large{A}})}$
= 2⁴ = 2 × 2 × 2 × 2 = 16

Hence, number of binary operation on set A = 16

Answer 2

Answer:

Hence, number of binary operations defined on set A = 16

Step-by-step explanation:

Let A = {5, 6}

Number of elements in the set A, n = 2

Number of relations in set having n is defined by : n²

⇒ number of relations in set A = 2² = 4

Now, number of binary relations is defined by :

$n^n^2$

⇒ Number of binary operations in set A =

$2^4=16$

Hence, number of binary operations defined on set A = 16