Question

The number of binaly operations on {1, 2} is......,Select Proper option from the given options.
(a) 16
(b) 8
(c) 2
(d) 4

Answer 1

Dear student ,

Answer: Option a (16)

Solution:

If A is a set has n elements, then ,total number of binary operations on that set us equal to the number of functions from A x A to A.

Also the total number of functions from a finite set X to a finite set Y =
$( {n(y)})^{n(x)}$

Hence the total number of binary operations on set A =
${n}^{ {n}^{2} }$

Here,{1,2}

Total elements are 2

Number of binary operations =
${2}^{ {2}^{2} } \\ \\ = {2}^{4} \\ = 16$
Answer is 16.

Hope it helps you.