Write the converse, inverse and contrapositive of the following statements.
you will be strong only if you drink your milk.

Answer

To solve the problem, we need to identify the original statement and then derive its converse, inverse, and contrapositive.

### Original Statement:
"You will be strong only if you drink your milk."

This can be expressed in logical terms as:
- Let \( p \): "You are strong."
- Let \( q \): "You drink your milk."

The original statement can be written as:
\[ p \implies q \]
This means "If you are strong, then you drink your milk."

### Step 1: Converse
The converse of a statement \( p \implies q \) is \( q \implies p \).

**Converse:** "If you drink your milk, then you are strong."
\[ q \implies p \]

### Step 2: Inverse
The inverse of a statement \( p \implies q \) is \( \neg p \implies \neg q \).

**Inverse:** "If you are not strong, then you do not drink your milk."
\[ \neg p \implies \neg q \]

### Step 3: Contrapositive
The contrapositive of a statement \( p \implies q \) is \( \neg q \implies \neg p \).

**Contrapositive:** "If you do not drink your milk, then you are not strong."
\[ \neg q \implies \neg p \]

### Final Answers:
- **Converse:** If you drink your milk, then you are strong.
- **Inverse:** If you are not strong, then you do not drink your milk.
- **Contrapositive:** If you do not drink your milk, then you are not strong.

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