`(p ^^ q) vv r = (p vv r) ^^` ........

Answer

To solve the equation \((p \land q) \lor r = (p \lor r) \land ?\), we will use the properties of logical operations, specifically the distributive property.

### Step-by-step Solution:

1. **Understand the Left Side**: The left side of the equation is \((p \land q) \lor r\). This expression states that either both \(p\) and \(q\) are true, or \(r\) is true.

2. **Apply Distributive Property**: According to the distributive property of logical operations, we can rewrite the left side. The distributive property states that:
\[ A \lor (B \land C) = (A \lor B) \land (A \lor C) \]
In our case, we can think of \(r\) as being distributed over the conjunction \(p \land q\).

3. **Rearranging the Expression**: We can rewrite the left side as:
\[ (p \land q) \lor r = (p \lor r) \land (q \lor r) \]
This means that for the left side to be true, either \(p\) must be true or \(r\) must be true, and either \(q\) must be true or \(r\) must be true.

4. **Identify the Missing Term**: From the rearranged expression, we can see that the right side \((p \lor r) \land ?\) must equal \((p \lor r) \land (q \lor r)\). Therefore, the missing term in the equation is \(q \lor r\).

5. **Final Answer**: Thus, we conclude that:
\[ (p \land q) \lor r = (p \lor r) \land (q \lor r) \]
Hence, the answer for the question is \(q \lor r\).