Question

We have learned that addition and multiplication are both commutative operations.

(a) Is subtraction commutative?

(b) Is division of nonzero real numbers commutative?

(c) Are the actions of putting on your socks and putting on your shoes commutative?

(d) Are the actions of putting on your hat and putting on your coat commutative? (e) Are the actions of washing laundry and drying it commutative?

Short answer

1. Subtraction is not commutative
2. Division of nonzero real numbers is not commutative
3. Actions of putting on your socks and putting on your shoes is not commutative
4. Actions of putting on your hat and putting on your coatiscommutative

Actions of washing laundry and drying it is not commutative

Step-by-step solution

. Apply the concept of commutative operations

Any operation * is commutative if$a*b=b*a$

. Analyze the given operation

Given operation is subtraction.

. Check whether the given operation is commutative or not

Let us assume that subtraction is commutative.

Consider two numbers 3 and 5.

Applying the operation on them, we get:

$\begin{array}{l}3-5=-2\\ 5-3=2\\ 2\ne -2\\ \Rightarrow 3-5\ne 5-3\end{array}$

So, our assumption that subtraction is commutative is not true.

Therefore, subtraction is not commutative

. Apply the concept of commutative operations

Any operation * is commutative if$a*b=b*a$

. Analyze the given operation

Given operation is division.

. Check whether the given operation is commutative or not

Let us assume that division of nonzero real numbers is commutative.

Consider two numbers 2 and 4.

Applying the operation on them, we get:

$\begin{array}{l}2÷4=\frac{1}{2}\\ 4÷2=2\\ 2\ne \frac{1}{2}\\ \Rightarrow 2÷4\ne 4÷2\end{array}$

So, our assumption that division of nonzero real numbers is commutative is not true.

Therefore, division of nonzero real numbers is not commutative.

. Apply the concept of commutative operations

Any operation * is commutative if$a*b=b*a$

. Analyze the given operation

Given operation is “action of putting on”

Step 3  .Check whether the given operation is commutative or not

Action of putting on your socks first and then putting on your shoes is what we do generally. It has socks inside the shoes.

Now, action of putting on your shoes first and then putting on your socks would include putting on socks over the shoes. It has socks outside the shoes, which is not same as the action of putting on your socks first and then putting on your shoes.

So, actions of putting on your socks and putting on your shoes is not commutative.

. Apply the concept of commutative operations

Any operation * is commutative if$a*b=b*a$

. Analyze the given operation

Given operation is “action of putting on”

. Check whether the given operation is commutative or not

Actions of putting on your hat first and then putting on your coat would end up having the hat on head and coat on vest.

Now, action of putting on your coat first and then putting on your hat would also end up having the hat on head and coat on vest.

So, actions of putting on your hat and putting on your coat is commutative.

. Apply the concept of commutative operations

Any operation * is commutative if$a*b=b*a$

. Analyze the given operation

Given operation is “action of”

. Check whether the given operation is commutative or not

Let us assume we have a dryer and a washer.

Actions of washing laundry first and then drying it would include putting dirty clothes in washer first where we get wet clothes after washing and then putting wet clothes in dryer ending up getting dried clothes.

Now, actions of drying laundry first and then washing it would include putting dirty clothes in dryer first where we get dried clothes after drying and then putting dried clothes in washer ending up getting wet clothes, is not same as getting dried clothes out if we do actions of washing laundry first and then drying it.

So, actions of washing laundry and drying it is not commutative.