Let p `:` 'He is rich' and q `:` 'He is happy' be the given statements. Write each of the following statements in the symbolic form, using p and q.
It is necessary to be happy in order to be poor.

Answer

To convert the statement "It is necessary to be happy in order to be poor" into symbolic form using the given statements \( p \) and \( q \), we can follow these steps:

### Step 1: Understand the Statements
- Let \( p \) represent "He is rich."
- Let \( q \) represent "He is happy."

### Step 2: Analyze the Given Statement
The statement "It is necessary to be happy in order to be poor" can be interpreted as:
- Being happy (\( q \)) is a necessary condition for being poor (not rich, which is represented as \( \neg p \)).

### Step 3: Rewrite the Statement
The phrase "It is necessary to be happy in order to be poor" can be rephrased as:
- If he is poor (not rich), then he must be happy.
- This can be expressed as: If \( \neg p \) (not rich), then \( q \) (happy).

### Step 4: Symbolic Representation
Using the implication form, we can write:
- \( \neg p \implies q \)

### Step 5: Final Symbolic Form
Thus, the symbolic form of the statement "It is necessary to be happy in order to be poor" is:
- \( \neg p \implies q \)