`~| (p vv q)` = .......

Answer

To solve the expression `~| (p ∨ q)`, we will use De Morgan's Law. Here’s a step-by-step solution:

### Step 1: Identify the expression
We start with the expression `~(p ∨ q)`, where `~` represents negation and `∨` represents disjunction (logical OR).

**Hint:** Recognize the components of the expression: negation and disjunction.

### Step 2: Apply De Morgan's Law
According to De Morgan's Law, the negation of a disjunction can be expressed as the conjunction of the negations. Specifically, it states that:
\[ \sim (p \lor q) \equiv \sim p \land \sim q \]
This means that the negation of `p ∨ q` is equivalent to `¬p ∧ ¬q`.

**Hint:** Remember that De Morgan's Law transforms a disjunction into a conjunction while negating each component.

### Step 3: Write the final expression
Using De Morgan's Law, we can rewrite the original expression:
\[ ~(p ∨ q) = \sim p \land \sim q \]

**Hint:** Ensure you apply the law correctly by negating both parts of the disjunction.

### Final Answer
Thus, the expression `~(p ∨ q)` is equivalent to:
\[ \sim p \land \sim q \]

### Summary of Steps
1. Identify the expression as negation of a disjunction.
2. Apply De Morgan's Law to transform the expression.
3. Write the final equivalent expression.