# 04 - Commutation

1. The commutative law is the same as the associative law. They are different names for the same thing.

False

True

2. The Commutative law states that: A + A = A

TRUE

FALSE

3. Which of the following are expressions of the Commutative law?
```A + B = B + A
A B = B A
A + BC = BC + AB
A + BC = ABC```

The first one

Only the last two

The first two

All of them

4. According to the Commutative law, A + B is equal to B + A and A + B can also be equal to AB

TRUE

FALSE

5. Fill in the blanks in the following diagram illustrating commutation

B+A = A+B

A.B = B.A

A.B = A

A.B =B.B

6. Decide if the following statement is true or false.
```a + b = b + a.

The operation is associative because
the order of the elements does not affect
the result of the operation.

The commutative property,concerns the grouping
of elements in an operation and is
always identical to association```

FALSE

TRUE

7. Simply put, the commutative property states that the factors in an equation can be rearranged freely without affecting the outcome of the equation

TRUE

FALSE

8. The commutative property can be expressed through the equations a + b = b + a and a x b = b x a. No matter the order of the values in these equations, the _____ will always be the same.

gates

results

errors

inputs

9. We can tell the difference between the associative and the commutative property by asking the question, “Are we changing the order of the elements, or are we changing the grouping of the elements?
```If the elements are being reordered,
then the commutative property applies.

If the elements are only being regrouped,
then the associative property applies.```

FALSE

TRUE

10. Decide whether the following statement is true or false.
```However, note that the presence of parentheses
alone does not necessarily mean that the
property applies. For instance:

(2 + 3) + 4 = 4 + (2 + 3)

This equation is an example of the
commutative property