Write 'T' for True and 'F' for False.
`(p implies q) vv (r implies p)` is a tautology.

Answer

To determine whether the statement `(p implies q) vv (r implies p)` is a tautology, we will create a truth table and analyze the truth values of the components involved.

### Step 1: Identify the components
The statement consists of two parts:
1. \( p \implies q \)
2. \( r \implies p \)

We will evaluate the truth values of these implications based on all possible combinations of truth values for \( p \), \( q \), and \( r \).

### Step 2: Create a truth table
We will create a truth table with columns for \( p \), \( q \), \( r \), \( p \implies q \), \( r \implies p \), and finally the expression \( (p \implies q) \vee (r \implies p) \).

| \( p \) | \( q \) | \( r \) | \( p \implies q \) | \( r \implies p \) | \( (p \implies q) \vee (r \implies p) \) |
|---------|---------|---------|---------------------|---------------------|------------------------------------------|
| T | T | T | T | T | T |
| T | T | F | T | T | T |
| T | F | T | F | T | T |
| T | F | F | F | T | T |
| F | T | T | T | F | T |
| F | T | F | T | F | T |
| F | F | T | T | F | T |
| F | F | F | T | T | T |

### Step 3: Analyze the truth values
- The implication \( p \implies q \) is false only when \( p \) is true and \( q \) is false. In all other cases, it is true.
- The implication \( r \implies p \) is false only when \( r \) is true and \( p \) is false. In all other cases, it is true.
- The disjunction \( (p \implies q) \vee (r \implies p) \) is true unless both \( p \implies q \) and \( r \implies p \) are false.

### Step 4: Conclusion
From the truth table, we see that the last column, which represents the expression \( (p \implies q) \vee (r \implies p) \), is true for all combinations of truth values for \( p \), \( q \), and \( r \). Therefore, the statement is always true.

Thus, we conclude that the statement `(p implies q) vv (r implies p)` is a tautology, and we write 'T' for True.

### Final Answer
The truth value of the statement is **T**.