If p: Sam is fat,q : Sam is happy,indicate the symbolic form of the following verbal statements
Sam is thin but happy.

Options

A. `~pvvq`
B. `pvv~q`
C. `p^^~q`
D. `~p^^q`

Answer

To convert the verbal statement "Sam is thin but happy" into symbolic form using the given definitions of p and q, we can follow these steps:

1. **Identify the Statements**:
- Let \( p \): "Sam is fat"
- Let \( q \): "Sam is happy"

2. **Determine the Negation of p**:
- Since "Sam is thin" is the opposite of "Sam is fat", we can express "Sam is thin" as \( \neg p \) (the negation of p).

3. **Express "but happy"**:
- The phrase "but happy" indicates that Sam is happy, which can be expressed as \( q \).

4. **Combine the Statements**:
- The conjunction "but" in logical terms is represented as "and". Therefore, we combine the two statements using the logical conjunction operator \( \land \).
- This gives us the symbolic form: \( \neg p \land q \).

Thus, the symbolic form of the statement "Sam is thin but happy" is \( \neg p \land q \).