Is {x : x is a factor of 27} `ne` {3, 9, 27, 54} ? Give reason.

Answer

To determine if the sets {x : x is a factor of 27} and {3, 9, 27, 54} are equal, we will follow these steps:

### Step 1: Identify the factors of 27
First, we need to find the factors of 27. A factor is a number that divides another number without leaving a remainder.

The factors of 27 are:
- 1 (27 ÷ 1 = 27)
- 3 (27 ÷ 3 = 9)
- 9 (27 ÷ 9 = 3)
- 27 (27 ÷ 27 = 1)

Thus, the set of factors of 27 is:
**Set A = {1, 3, 9, 27}**

### Step 2: Identify the elements of the second set
The second set given is:
**Set B = {3, 9, 27, 54}**

### Step 3: Compare the two sets
To determine if two sets are equal, all elements of Set A must be present in Set B, and all elements of Set B must be present in Set A.

- **Elements of Set A**: {1, 3, 9, 27}
- **Elements of Set B**: {3, 9, 27, 54}

Now, let's compare:
- Set A has the element **1**, which is **not** in Set B.
- Set B has the element **54**, which is **not** in Set A.

### Step 4: Conclusion
Since there are elements in Set A that are not in Set B and vice versa, we conclude that:
**Set A is not equal to Set B**.

Therefore, the answer to the question is:
**{x : x is a factor of 27} is not equal to {3, 9, 27, 54}.**