Simplifying logic circuit
Using deMorgan's symbols for \$T_4\$, \$T_5\$ &amp; \$T_6\$.  A NAND is a negative OR.



$$F = \bar A + \overline {\overline {ABC}} + \overline {\overline {BC}}$$

$$F = \bar A + ABC + BC$$

$$F = \bar A + BC$$

$$ G = \overline {(\bar A + BC)(\overline {\overline {ABC}} + \bar B + \overline {\overline {BCD}})(\overline {\overline {BC}} + \overline {\overline {BCD}} + \bar D)} $$
$$ G = \overline {(\bar A + BC)(ABC + \bar B + BCD)(BC + BCD + \bar D)} $$
$$ G = \overline {(\bar A + BC)(ABC + \bar B + BCD)(BC + \bar D)} $$
$$ G = \overline {(\bar A D + BC)(ABC + \bar B + BCD)} $$

G can still be simplified.  Otherwise check the math.

But deMorgan's can simplify the process if applied correctly.