`~(p ^^ q)` is equal to-

Options

A. `~p vv ~q`
B. `~p ^^~q`
C. `~ p ^^q`
D. `p ^^ ~q`

Answer

To solve the expression `~(p ∧ q)`, we will use De Morgan's Law, which states that the negation of a conjunction is equivalent to the disjunction of the negations.

### Step-by-Step Solution:

1. **Identify the Expression**: We start with the expression `~(p ∧ q)`, where `~` denotes negation and `∧` denotes logical AND.

2. **Apply De Morgan's Law**: According to De Morgan's Law, the negation of a conjunction can be expressed as the disjunction of the negations. Therefore, we can rewrite the expression as:
\[ ~(p ∧ q) = ~p ∨ ~q \]
This means that the negation of `p AND q` is equivalent to `NOT p OR NOT q`.

3. **Final Result**: Thus, the expression `~(p ∧ q)` is equal to `~p ∨ ~q`.

### Summary:
The final answer is:
\[ ~(p ∧ q) = ~p ∨ ~q \]