The converse of the statement If `xgty`, then `x+agty+a` is

Options

A. (a) If `xlty` then `x=alty+a`
B. (b) If `(x+a)gt(y+a)` then `xgty`
C. (c) If `xlty` then `x+agty+a`
D. (d) If `xgty` then `x+alty+a`

Answer

To find the converse of the statement "If \( x > y \), then \( x + a > y + a \)", we will follow these steps:

### Step 1: Identify the original statement
The original statement can be expressed in the form of an implication:
- Let \( P \): \( x > y \)
- Let \( Q \): \( x + a > y + a \)

Thus, the original statement is \( P \implies Q \).

### Step 2: Write the converse
The converse of an implication \( P \implies Q \) is \( Q \implies P \). Therefore, we need to express the converse:
- The converse will be: "If \( x + a > y + a \), then \( x > y \)".

### Step 3: Analyze the converse statement
Now we can write the converse statement clearly:
- If \( x + a > y + a \), then \( x > y \).

### Step 4: Match with the options
Now, we need to check which of the given options matches our converse statement:
- Option A: If \( x < y \), then \( x = y + a \)
- Option B: If \( x + a > y + a \), then \( x > y \)
- Option C: If \( x < y \), then \( x + a > y + a \)
- Option D: If \( x > y \), then \( x + a < y + a \)

From the options, we can see that option B matches our derived converse statement.

### Conclusion
Thus, the correct answer is:
**Option B: If \( x + a > y + a \), then \( x > y \)**.

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