The maximum number of compound propositions, out of $$p \vee r \vee s$$, $$p \vee r \vee \sim s$$, $$p \vee \sim q \vee s$$, $$\sim p \vee \sim r \vee s$$, $$\sim p \vee \sim r \vee \sim s$$, $$\sim p \vee q \vee \sim s$$, $$q \vee r \vee \sim s$$, $$q \vee \sim r \vee \sim s$$, $$\sim p \vee \sim q \vee \sim s$$ that can be made simultaneously true by an assignment of the truth values to $$p, q, r$$ and $$s$$, is equal to

We need to find the maximum number of the 9 given compound propositions that can be made simultaneously true by assigning truth values to $$p, q, r, s$$.

The 9 propositions are:

1. $$p \vee r \vee s$$   2. $$p \vee r \vee \sim s$$   3. $$p \vee \sim q \vee s$$

4. $$\sim p \vee \sim r \vee s$$   5. $$\sim p \vee \sim r \vee \sim s$$   6. $$\sim p \vee q \vee \sim s$$

7. $$q \vee r \vee \sim s$$   8. $$q \vee \sim r \vee \sim s$$   9. $$\sim p \vee \sim q \vee \sim s$$

Strategy:

There are $$2^4 = 16$$ possible truth value assignments for $$(p, q, r, s)$$. A disjunction (OR) is false only when all its operands are false. We systematically check assignments to maximize the count of true propositions.

Try $$p = T,\; q = T,\; r = F,\; s = F$$:

Evaluate each proposition:

1. $$T \vee F \vee F = T$$ $$\checkmark$$

2. $$T \vee F \vee T = T$$ $$\checkmark$$

3. $$T \vee F \vee F = T$$ $$\checkmark$$

4. $$F \vee T \vee F = T$$ $$\checkmark$$

5. $$F \vee T \vee T = T$$ $$\checkmark$$

6. $$F \vee T \vee T = T$$ $$\checkmark$$

7. $$T \vee F \vee T = T$$ $$\checkmark$$

8. $$T \vee T \vee T = T$$ $$\checkmark$$

9. $$F \vee F \vee T = T$$ $$\checkmark$$

All 9 propositions are true.

Verify this is indeed the maximum:

Since all 9 propositions are satisfied by the assignment $$(p, q, r, s) = (T, T, F, F)$$, the maximum possible number is 9.

The answer is $$\boxed{9}$$.