Find, which of the following sets are singleton sets :
A={x : 7x -3=11}`

Answer

To determine if the set \( A = \{ x : 7x - 3 = 11 \} \) is a singleton set, we will follow these steps:

### Step 1: Solve the equation
We start with the equation given in the set definition:
\[ 7x - 3 = 11 \]
To isolate \( x \), we first add 3 to both sides:
\[ 7x = 11 + 3 \]
This simplifies to:
\[ 7x = 14 \]

### Step 2: Divide by 7
Next, we divide both sides by 7 to solve for \( x \):
\[ x = \frac{14}{7} \]
This simplifies to:
\[ x = 2 \]

### Step 3: Define the set
Now that we have found the value of \( x \), we can define the set \( A \):
\[ A = \{ 2 \} \]

### Step 4: Check if it is a singleton set
A singleton set is defined as a set that contains exactly one element. Since our set \( A \) contains only the element 2, we conclude that:
\[ A \text{ is a singleton set.} \]

### Final Answer
Yes, the set \( A \) is a singleton set.

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