Question

Determine whether the given expression is a binary

operation or not. Explain your answer through narration

and/or computation.

1.Addition on { 0, 1, 2}

2.Division on rational numbers (Q)

3.Addition on whole number (W)

4.Multiplication on the complex numbers (C)

5. Subtraction on prime numbers (P)

6.Multiplication on integers (Z)​

Answer 1

Step-by-step explanation:

Definition A binary operation ∗ on a set A is an operation which, when applied to any elements x and y of the set A, yields an element x ∗ y of A. ... However the operation of subtraction is not commutative, since x − y = y − x in general. (Indeed the identity x − y = y − x holds only when x = y.)

Answer 2

Answer:

Given,

1.Addition on { 0, 1, 2}

2. Division on rational numbers (Q)

3. Addition on whole number (W)

4. Multiplication on the complex numbers (C)

5. Subtraction on prime numbers (P)

6. Multiplication on integers (Z)​

To Find,

Which out of the given expressions is a binary operation.

Solution,

We can simply solve this by going through the expressions one by one.

1. Addition is a binary operation when performed between two numbers. but here the operation is between three numbers. So, this expression is not binary.

2. Division is also a binary operation when performed on two numbers. But here we are referring to more than two numbers. So, this expression is not binary.

3. Addition is a binary operation when performed between two numbers. but here the operation is between more than two numbers. So, this expression is not binary.

4. Multiplication is a binary operation when performed between two numbers. but here the operation is between more than two numbers. So, this expression is not binary.

5. Subtraction is a binary operation when performed between two numbers. but here the operation is between more than two numbers. So, this expression is not binary.

6. Multiplication is a binary operation when performed between two numbers. but here the operation is between more than two numbers. So, this expression is not binary.

Hence, none of these is a binary operation.