Attempt the following
Write the negation of `p rarr q`

Answer

To find the negation of the statement \( p \rightarrow q \) (which reads as "if \( p \) then \( q \)"), we can follow these steps:

### Step 1: Understand the implication
The implication \( p \rightarrow q \) can be understood in terms of its truth values. It is only false when \( p \) is true and \( q \) is false. In all other cases, it is true.

### Step 2: Write the truth table for \( p \rightarrow q \)
| \( p \) | \( q \) | \( p \rightarrow q \) |
|---------|---------|-----------------------|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |

From the truth table, we see that \( p \rightarrow q \) is false only when \( p \) is true and \( q \) is false.

### Step 3: Write the negation
The negation of \( p \rightarrow q \) is the condition under which \( p \rightarrow q \) is false. Therefore, the negation can be expressed as:
\[ \neg(p \rightarrow q) \equiv p \land \neg q \]

### Step 4: Conclusion
Thus, the negation of \( p \rightarrow q \) is \( p \land \neg q \).