` ~[ p vv (~q)]` is equal to-

Options

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

Answer

To solve the expression `~[p ∨ (~q)]`, we will apply De Morgan's laws and logical equivalences step by step.

### Step-by-Step Solution:

1. **Identify the Expression**:
We start with the expression `~[p ∨ (~q)]`.

2. **Apply De Morgan's Law**:
According to De Morgan's laws, the negation of a disjunction is equivalent to the conjunction of the negations. Thus, we can rewrite the expression as:
\[ ~[p ∨ (~q)] = ~p ∧ ~~q \]

3. **Simplify Double Negation**:
The double negation `~~q` simplifies to `q`. Therefore, we have:
\[ ~p ∧ q \]

4. **Final Result**:
The expression `~[p ∨ (~q)]` simplifies to `~p ∧ q`.

### Conclusion:
The expression `~[p ∨ (~q)]` is equal to `~p ∧ q`.

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