For any statements p and q , the statement `~(~p^^q)` is equivalent to

Options

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

Answer

To solve the problem of finding the equivalent statement for `~(~p ∧ q)`, we will use logical equivalences step by step.

### Step 1: Identify the expression
We start with the expression:
\[ \sim(\sim p \land q) \]

### Step 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:
\[ \sim(\sim p \land q) = \sim(\sim p) \lor \sim(q) \]

### Step 3: Simplify the negation
Now, we simplify the negation of `~p`:
\[ \sim(\sim p) = p \]
Thus, the expression becomes:
\[ p \lor \sim q \]

### Final Answer
The statement `~(~p ∧ q)` is equivalent to:
\[ p \lor \sim q \]