If p : A man is happy and
q : A man is rich
Then, the statement ''If a man is not happy, then he is not rich'' is written as

Options

A. `~p to ~q`
B. `~ q to p`
C. `~q to ~ p`
D. `q to ~ p`

Explanation

To convert the statement "If a man is not happy, then he is not rich" into a mathematical form using the given propositions, we can follow these steps:

### Step 1: Identify the Statements
Let:
- \( p \): A man is happy
- \( q \): A man is rich

### Step 2: Negate the Statements
The statement "a man is not happy" translates to the negation of \( p \), which is written as \( \neg p \).
Similarly, "he is not rich" translates to the negation of \( q \), which is written as \( \neg q \).

### Step 3: Formulate the Implication
The original statement is an "if-then" statement. In logical terms, this is represented by the implication symbol \( \rightarrow \).

Thus, the statement "If a man is not happy, then he is not rich" can be expressed as:
\[ \neg p \rightarrow \neg q \]

### Final Answer
The mathematical form of the statement "If a man is not happy, then he is not rich" is:
\[ \neg p \rightarrow \neg q \]

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