To minimize the given Boolean function $F(P, Q, R, S) = \pi(3, 5, 7, 8, 10, 11, 12, 13)$ to the Product of Sums (PoS) form, we'll follow these steps:

1. List the minterms: First, convert the maxterm indices to the minterms that are missing from the range (0 to 15).

2. Group the missing minterms: These missing minterms will help us identify the minterms that should be 1 in the Truth Table.

3. Karnaugh Map (K-map) analysis: Place the 0s (from the given indices) on the K-map to find simplified sum terms.

4. Find the simplified maxterms from the K-map to obtain the PoS expression.

Step-by-step Solution:

1. Convert maxterms to minterms:

   • Maxterms given: $\pi (3, 5, 7, 8, 10, 11, 12, 13)$
   • Minterms are all terms from 0 to 15 not listed above, which are:
     $m(0, 1, 2, 4, 6, 9, 14, 15)$.

2. Create the K-map and place 0s for the given maxterms:

   • 2-variable map with P and Q as the row variables and R and S as the column variables.

PQ\RS	00	01	11	10
00	1	1	0	0
01	1	0	0	1
11	0	0	0	1
10	0	1	1	0

3. Identify groups of 0s and derive the maxterms from the map. The grouping will help simplify the expression:

   • Group 1: Maxterms that cover columns RS = 00 → (P + R)
   • Group 2: Row 01 with column RS = 11 → $(P + S)$
   • Group 3: RS = 10, PQ = 11 and PQ = 10 → (Q + R)

4. Simplified PoS: So, the minimized function in Product of Sum form is:

$F(P, Q, R, S) = (P + R)(P + S)(Q + R)$

Do you need further clarifications?

Here are some further questions for exploring the concept:

1. What is the meaning of maxterm in Boolean functions?
2. How do minterms and maxterms relate?
3. Can you create a truth table for the simplified PoS?
4. How is the grouping performed in the Karnaugh map?
5. Why PoS forms are useful in digital circuits?

Tip: Always check your simplified result by creating truth tables to verify logic validity!