Step 1: Understanding the Concept:
Bovine venereal trichomoniasis (Tritrichomonas foetus) causes early embryonic death, post-coital vaginitis, and post-coital pyometra with characteristic odorless, thin, yellowish-grey discharge.
Step 2: Detailed Explanation:
1. Statement I: In bovine venereal trichomoniasis (Tritrichomonas foetus), infection of the uterine cavity following coital transmission produces large volumes (up to $5 - 10\text{ litres}$) of an odorless, thin, yellowish-grey, flocculent uterine exudate clinically designated as 'Potato-Soup Discharge'. Hence, Statement I is true.
2. Statement II: Tritrichomonas foetus causes embryonic death at 1--2 months of gestation; persistence of the corpus luteum with closed cervix leads to Post-coital Bovine Pyometra. Hence, Statement II is true.
Step 3: Final Answer:
Therefore, Both Statement I and Statement II are true, matching option (A).