If p is true and q is false, then which of the following statements is NOT true ?

Options

A. `pvvq`
B. `p^^(~q)`
C. `pto p`
D. `ptoq`

Explanation

To solve the problem, we need to evaluate the truth values of various logical statements based on the given conditions: P is true (T) and Q is false (F). We will analyze each option step by step to determine which statement is NOT true.

### Step-by-Step Solution:

1. **Understanding the Variables**:
- We have two variables: P and Q.
- Given: P = True (T), Q = False (F).

2. **Identifying the Logical Operations**:
- We will evaluate the following logical operations:
- Disjunction (P ∨ Q)
- Conjunction (P ∧ ¬Q)
- Conditional (P → Q)
- Conditional (P → P)

3. **Evaluating Each Statement**:
- **Statement 1: P ∨ Q (P or Q)**:
- Since P is true (T) and Q is false (F), the disjunction is:
- T ∨ F = T (True)

- **Statement 2: P ∧ ¬Q (P and not Q)**:
- First, we find ¬Q (negation of Q):
- ¬Q = T (since Q is F)
- Now evaluate the conjunction:
- T ∧ T = T (True)

- **Statement 3: P → Q (P implies Q)**:
- This is a conditional statement. It is false only if P is true and Q is false:
- T → F = F (False)

- **Statement 4: P → P (P implies P)**:
- This is always true, as any statement implies itself:
- T → T = T (True)

4. **Identifying the Statement that is NOT True**:
- From our evaluations:
- Statement 1: True
- Statement 2: True
- Statement 3: False
- Statement 4: True
- The only statement that is NOT true is **Statement 3: P → Q**.

### Conclusion:
The statement that is NOT true is **P → Q**.