# How many binary operations are possible on a set?

Table of Contents

- 1 How many binary operations are possible on a set?
- 2 How many different binary operations can be defined on a set with N elements hint think about filling in a table?
- 3 How many binary operations are there on a set with 2 elements?
- 4 How many binary operations does a set of 5 elements have?
- 5 Which one of the following is the possible number of binary operations defined on the set A ={ a B?
- 6 How many binary operations have any element as an identity?

## How many binary operations are possible on a set?

For a set of two elements there are 2^4 = 16 different binary operations.

### How many different binary operations can be defined on a set with N elements hint think about filling in a table?

Things I know: There are exactly nn2 different binary operations on any given finite set of n elements.

**How many different binary operations are possible on a set of 3 elements?**

19,683

As mentioned in the introduction, the number of possible binary operations on a set of three elements is 19,683. Of these 729 are commutative and for 243 different operations there exists an identity, and likewise for 243 operations there exists a zero.

**How many different commutative binary operations can be defined on a set S with exactly 3 elements?**

OPERATIONS ON A SET WITH THREE ELEMENTS As mentioned in the introduction, the number of possible binary operations on a set of three elements is 19683. Of these 729 are commutative.

## How many binary operations are there on a set with 2 elements?

Of the 16 binary operations on a two element set, which ones are commutative, associative, have an identity element, and have inverse?

### How many binary operations does a set of 5 elements have?

298,023,223,876,953,125

As mentioned in the introduction, the number of possible binary operations on a set of five elements is 298,023,223,876,953,125.

**How many binary operations can be defined on a set with 5 elements?**

To prove this is an easy calculation; there are five different answers for each of the 25 seats of a 5Χ5 operation table so the number of distinct binary operations is 525 .

**How many binary operation can be defined on a set with 2 elements?**

## Which one of the following is the possible number of binary operations defined on the set A ={ a B?

Hence, the total number of binary operations on the set {a, b} is 24 i.e., 16.

### How many binary operations have any element as an identity?

two binary operations

Note that 0+a = a+0 = a for all a ∈ Z. Also note that 1×a = a×1 = a for all a ∈ Z. These two binary operations are said to have an identity element.

**What is commutative binary operation?**

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. The idea that simple operations, such as the multiplication and addition of numbers, are commutative was for many years implicitly assumed.