Given below is a statement followed by two conclusions I and II. Study the statement carefully and decide which Conclusion/s is/are definitely true.
Statement: $$A \geq B \geq C = D < E; F \leq C > G$$
Conclusion I: $$A \geq F$$
Conclusion II: $$D > G$$

The given statement contains two separate comparison chains.

First chain: $$A \geq B \geq C = D \lt E$$
Second chain: $$F \le C \gt G$$

Rewrite each chain in words so that every link is clear:
1. $$A \ge B$$, $$B \ge C$$, $$C = D$$, $$D \lt E$$.
2. $$F \le C$$, $$C \gt G$$.

Checking Conclusion I: $$A \ge F$$

Step-1: From the second chain $$F \le C$$ can be reversed as $$C \ge F$$.

Step-2: The first chain already gives $$A \ge C$$.

Step-3: Combine the two results:
$$A \ge C \quad\text{and}\quad C \ge F \;\; \Rightarrow \;\; A \ge F.$$

Thus Conclusion I is definitely true.

Checking Conclusion II: $$D \gt G$$

Step-1: From the first chain $$C = D$$ (so $$D = C$$).

Step-2: From the second chain $$C \gt G$$.

Step-3: Replace $$C$$ by $$D$$ (because $$C = D$$):
$$D = C \gt G \;\; \Rightarrow \;\; D \gt G.$$

Thus Conclusion II is also definitely true.

Both conclusions follow with certainty.

Therefore, the correct choice is:
Option D which is: Both Conclusions I and II are true.