Assume that two given statements p and q are both true and indicate whether or not you would expect each of the following statements to be true :
`(~p)vv(~q)`

Answer

To determine the truth value of the statement \( (~p) \lor (~q) \) given that both statements \( p \) and \( q \) are true, we can follow these steps:

### Step 1: Understand the Given Statements
We are given that:
- \( p \) is true (denoted as 1)
- \( q \) is true (denoted as 1)

### Step 2: Find the Negations
Next, we need to find the negations of \( p \) and \( q \):
- The negation of \( p \) is \( ~p \). Since \( p \) is true, \( ~p \) will be false (denoted as 0).
- The negation of \( q \) is \( ~q \). Since \( q \) is true, \( ~q \) will also be false (denoted as 0).

### Step 3: Evaluate the Union of Negations
Now, we need to evaluate the expression \( (~p) \lor (~q) \):
- We have \( ~p = 0 \) and \( ~q = 0 \).
- The union (logical OR) of \( ~p \) and \( ~q \) is \( 0 \lor 0 \).

### Step 4: Determine the Result
The result of \( 0 \lor 0 \) is 0, which means the expression \( (~p) \lor (~q) \) is false.

### Conclusion
Thus, the statement \( (~p) \lor (~q) \) is false when both \( p \) and \( q \) are true.

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