The solution set of `3x-4lt8` over the set of square numbers is

Options

A. {1,2,3}
B. {1,4}
C. {1}
D. {16}

Answer

To solve the inequality \(3x - 4 < 8\) and find the solution set over the set of square numbers, we can follow these steps:

### Step 1: Solve the Inequality
Start with the given inequality:
\[ 3x - 4 < 8 \]

### Step 2: Add 4 to Both Sides
To isolate the term with \(x\), add 4 to both sides:
\[ 3x < 8 + 4 \]
\[ 3x < 12 \]

### Step 3: Divide by 3
Now, divide both sides by 3 to solve for \(x\):
\[ x < \frac{12}{3} \]
\[ x < 4 \]

### Step 4: Identify Square Numbers Less Than 4
Now, we need to find square numbers that are less than 4. The square numbers are:
- \(0^2 = 0\)
- \(1^2 = 1\)
- \(2^2 = 4\)
- \(3^2 = 9\)

From these, the square numbers less than 4 are:
- \(0\)
- \(1\)

### Step 5: Conclusion
The solution set of \(3x - 4 < 8\) over the set of square numbers is:
\[ \{0, 1\} \]