Comprehension:
There are only four neighbourhoods in a city - Levmisto, Tyhrmisto, Pesmisto and Kitmisto. During the onset of a pandemic, the number of new cases of a disease in each of these neighbourhoods was recorded over a period of five days. On each day, the number of new cases recorded in any of the neighbourhoods was either $0,1,2$ or $3$.
The following facts are also known:
1. There was at least one new case in every neighbourhood on Day $1$.
2. On each of the five days, there were more new cases in Kitmisto than in Pesmisto.
3. The number of new cases in the city in a day kept increasing during the five-day period. The number of new cases on Day $3$ was exactly one more than that on Day $2$.
4. The maximum number of new cases in a day in Pesmisto was $2$, and this happened only once during the five-day period.
5. Kitmisto is the only place to have $3$ new cases on Day $2$.
6. The total numbers of new cases in Levmisto, Tyhrmisto, Pesmisto and Kitmisto over the five-day period were $12,12, 5$ and $14$ respectively.
Which of the two statements below is/are necessarily false?
Statement $\text{A}$: There were $2$ new cases in Tyhrmisto on Day $3$.
Statement $\text{B}$: There were no new cases in Pesmisto on Day $2$.
- Both Statement $\text{A}$ and Statement $\text{B}$
- Statement $\text{B}$ only
- Neither Statement $\text{A}$ nor Statement $\text{B}$
- Statement $\text{A}$ only