State whether the following sets are empty finite or infinite sets., mention the cardinal number.
{all colours of a rainbow}

Answer

To determine whether the set of all colors of a rainbow is empty, finite, or infinite, and to mention its cardinal number, we can follow these steps:

### Step 1: Identify the Set
The set we are considering is:
\[ S = \{ \text{all colors of a rainbow} \} \]

### Step 2: List the Colors of the Rainbow
A rainbow consists of seven distinct colors. These colors can be remembered using the acronym "VIBGYOR":
- V: Violet
- I: Indigo
- B: Blue
- G: Green
- Y: Yellow
- O: Orange
- R: Red

Thus, we can explicitly write the set as:
\[ S = \{ \text{Violet, Indigo, Blue, Green, Yellow, Orange, Red} \} \]

### Step 3: Determine if the Set is Empty, Finite, or Infinite
- An **empty set** has no elements.
- A **finite set** has a specific number of elements.
- An **infinite set** has an unlimited number of elements.

In this case, the set \( S \) contains seven colors, which is a specific number. Therefore, the set is a **finite set**.

### Step 4: Calculate the Cardinal Number
The **cardinal number** of a set is the number of elements in that set. Since there are seven colors in the rainbow, the cardinal number of set \( S \) is:
\[ \text{Cardinal Number} = 7 \]

### Final Answer
The set of all colors of a rainbow is a **finite set** with a cardinal number of **7**.

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