What do the product and sum symbols mean in digital systems?
\$∑\$ stands for SoP or Sum of Products.  The 1's in a truth-table.

\$∏\$ stands for PoS or Product of Sums.  The 0's in a truth table.

To illustrate the process: \$∑(0,1,4,7) = ∏(2,3,5,6)\$.

SoP (Minterms)

$$∑(0,1,4,7) = \overline A \overline B \overline C + \overline A \overline B C + A \overline B \overline C + ABC$$

Simplify:

$$∑(0,1,4,7) = \overline A \overline B + \overline B \overline C + ABC$$

PoS (Maxterms)

$$∏(2,3,5,6) = (A + \overline B + C)\ (A + \overline B + \overline C)\ (\overline A + B + \overline C)\ (\overline A + \overline B + C)$$

Multiply it out:

$$(AA + A \overline B + AC + A \overline B + \overline B \overline B  + \overline B C + A \overline C + \overline B \overline C + \overline C C) 
\ (\overline A + B + \overline C)\ (\overline A + \overline B + C)$$

Simplify:

$$(A + \overline B)\ (\overline A + B + \overline C)\ (\overline A + \overline B + C)$$

Multiply it out:

$$(A \overline A + A B + A \overline C + \overline A \overline B + \overline B B + \overline B \overline C)\ (\overline A + \overline B + C)$$

Simplify:

$$(A B + A \overline C + \overline A \overline B + \overline B \overline C)\ (\overline A + \overline B + C)$$

Multiply it out:

$$\overline A A B + \overline A A \overline C + \overline A\ \overline A \overline B + \overline A \overline B \overline C + A B \overline B + A \overline B \overline C + \overline A \overline B \overline B + \overline B \overline B \overline C + A B C + A \overline C C + \overline A \overline B C + \overline B \overline C C$$

Simplify:

$$\overline A \overline B + \overline B \overline C + ABC$$

$$∑(0,1,4,7) = \overline A \overline B + \overline B \overline C + ABC$$

$$∏(2,3,5,6) = \overline A \overline B + \overline B \overline C + ABC$$

So \$∑(0,1,4,7) = ∏(2,3,5,6)\$.

By a similar process you can show \$∑(0,3,4,6) = ∏(1,2,5,7)\$.