Write the converse, contradiction and contrapositive of the statement 'If x+3=9,then x=6.?

Answer

To solve the problem, we need to derive the converse, contradiction, and contrapositive of the given statement: "If \( x + 3 = 9 \), then \( x = 6 \)."

### Step 1: Identify the statements
Let:
- \( p \): \( x + 3 = 9 \)
- \( q \): \( x = 6 \)

### Step 2: Write the original statement
The original statement can be expressed as:
- If \( p \), then \( q \) (i.e., \( p \implies q \))

### Step 3: Write the converse
The converse of a statement \( p \implies q \) is \( q \implies p \).
- Converse: If \( x = 6 \), then \( x + 3 = 9 \).

### Step 4: Write the contradiction
The contradiction of a statement \( p \implies q \) is \( p \) and not \( q \) (i.e., \( p \land \neg q \)).
- Contradiction: \( x + 3 = 9 \) and \( x \neq 6 \).

### Step 5: Write the contrapositive
The contrapositive of a statement \( p \implies q \) is \( \neg q \implies \neg p \).
- Contrapositive: If \( x \neq 6 \), then \( x + 3 \neq 9 \).

### Summary of Results
1. **Converse**: If \( x = 6 \), then \( x + 3 = 9 \).
2. **Contradiction**: \( x + 3 = 9 \) and \( x \neq 6 \).
3. **Contrapositive**: If \( x \neq 6 \), then \( x + 3 \neq 9 \).

---