Let p be " I will marry her," and let q be " she is beautiful." Translate into symbolic form.
She is beautiful if and only if I will marry her.

Answer

To translate the statement "She is beautiful if and only if I will marry her" into symbolic form, we will follow these steps:

1. **Identify the statements**:
- Let \( p \) represent "I will marry her."
- Let \( q \) represent "She is beautiful."

2. **Understand the logical structure**:
- The phrase "if and only if" indicates a biconditional relationship between the two statements. This means that both statements are equivalent; if one is true, the other must also be true, and vice versa.

3. **Translate the statement**:
- The statement "She is beautiful if and only if I will marry her" can be expressed as:
\[ q \iff p \]
- Here, \( q \) (she is beautiful) is on the left side of the biconditional, and \( p \) (I will marry her) is on the right side.

4. **Final symbolic form**:
- Therefore, the symbolic form of the statement is:
\[ q \iff p \]