Rewrite each of the following statements in the form 'p if and only if q'.
Determine the truth value of each of the following statements `:`
`3+3 = 7` iff `5+2 =6`

Answer

To rewrite the statement "3 + 3 = 7" iff "5 + 2 = 6" in the form "p if and only if q", we will follow these steps:

### Step 1: Define the statements
Let:
- \( p \): "3 + 3 = 7"
- \( q \): "5 + 2 = 6"

### Step 2: Rewrite the statement
The statement can be rewritten in the form "p if and only if q" as:
\[ p \iff q \]
This translates to:
"3 + 3 = 7 if and only if 5 + 2 = 6".

### Step 3: Determine the truth values of p and q
Now, we need to evaluate the truth values of \( p \) and \( q \):
- For \( p \):
- \( 3 + 3 = 7 \) is **False** (since \( 3 + 3 = 6 \)).
- For \( q \):
- \( 5 + 2 = 6 \) is **False** (since \( 5 + 2 = 7 \)).

### Step 4: Evaluate the biconditional statement
The biconditional statement \( p \iff q \) is true if both \( p \) and \( q \) have the same truth values (both true or both false). Since both \( p \) and \( q \) are false, we have:
- \( p \iff q \) is **True**.

### Final Answer
The statement "3 + 3 = 7" iff "5 + 2 = 6" can be rewritten as:
"3 + 3 = 7 if and only if 5 + 2 = 6" and its truth value is **True**.

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