This is a truth table for the logical expression $(p \rightarrow q) \lor (r \rightarrow p)$, where $p$, $q$, and $r$ are propositions, and $\rightarrow$ stands for logical implication, and $\lor$ for logical disjunction (OR).

Let's break down the steps to fill in the table:

Logical Operations:

1. Implication ($p \rightarrow q$):

   • True unless $p$ is true and $q$ is false.

2. Implication ($r \rightarrow p$):

   • True unless $r$ is true and $p$ is false.

3. Disjunction ($A \lor B$):

   • True if either $A$ or $B$ is true, or both.

Let's evaluate each row:

Row 1: $p = V$, $q = V$, $r = V$

• $p \rightarrow q = V$
• $r \rightarrow p = V$
• $(p \rightarrow q) \lor (r \rightarrow p) = V$

Row 2: $p = V$, $q = V$, $r = F$

• $p \rightarrow q = V$
• $r \rightarrow p = V$
• $(p \rightarrow q) \lor (r \rightarrow p) = V$

Row 3: $p = V$, $q = F$, $r = V$

• $p \rightarrow q = F$
• (r \rightarrow p =