If x=5 and y=−2, then ` x−2y=9.` The contrapositive of this statement is/are

Answer

To find the contrapositive of the statement "If \( x = 5 \) and \( y = -2 \), then \( x - 2y = 9 \)", we will follow these steps:

### Step 1: Identify the components of the statement
We can break down the statement into three parts:
- Let \( p \): \( x = 5 \)
- Let \( q \): \( y = -2 \)
- Let \( r \): \( x - 2y = 9 \)

The original statement can be expressed as:
\[ p \land q \implies r \]
This means "If \( p \) and \( q \) are true, then \( r \) is true."

### Step 2: Write the negation of the conclusion and the premises
To form the contrapositive, we need to negate both the conclusion and the premises:
- The negation of \( r \) (which is \( x - 2y = 9 \)) is \( \neg r \): \( x - 2y \neq 9 \)
- The negation of \( p \) (which is \( x = 5 \)) is \( \neg p \): \( x \neq 5 \)
- The negation of \( q \) (which is \( y = -2 \)) is \( \neg q \): \( y \neq -2 \)

### Step 3: Formulate the contrapositive
The contrapositive of the statement is formed by reversing the implication and negating both sides:
\[ \neg r \implies \neg p \lor \neg q \]
This means:
"If \( x - 2y \neq 9 \), then \( x \neq 5 \) or \( y \neq -2 \)."

### Final Statement
Thus, the contrapositive of the original statement is:
"If \( x - 2y \neq 9 \), then \( x \neq 5 \) or \( y \neq -2 \)."

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