The converse of the statement:
If ` ( x ne y ) ` then ( x + a `ne ` y +a ) is

Options

A. If (x = y) then (x + a = y + a)
B. If (x `ne` y) then (x + a = y + a)
C. If `( x + a ne y + a ) " then " (x ne y ) `
D. If `(x + a ne y + a ) ` then ( x = y)

Answer

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

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

So, the original statement is:
\[ p \implies q \]
This reads as "If \( p \) is true, then \( q \) is true."

### Step 2: Write the converse
The converse of a statement \( p \implies q \) is formed by reversing the implication:
- The converse is \( q \implies p \)

In our case, this translates to:
\[ q \implies p \]
Which means:
"If \( x + a \neq y + a \), then \( x \neq y \)."

### Step 3: State the converse clearly
Thus, the converse of the original statement is:
"If \( x + a \neq y + a \), then \( x \neq y \)."

### Final Answer
The converse of the statement "If \( x \neq y \) then \( x + a \neq y + a \)" is:
"If \( x + a \neq y + a \), then \( x \neq y \)."

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