$(10$ points$).$ In $2016,$ Caterpillar purchased a large tract of land in Missouri with the intent to build a manufacturing facility thereon. At the start of construction in $2016,$ it was found that the land was contaminated with chemicals from a previous owner. Caterpillar has been fighting a long court battle to avoid having to pay for gieaning up the land. In $2018,$ Caterpillar wrote$-$off $($i$.$e$.,100\%$ impaired$)$ the value of the land, tid did not record anything regarding the possible clean$-$up$.$ In December $2020,$ as a result of a recent court decision, Caterpillar's board has decided that they had to record the approximately $$50$ million cost of cleaning up the land, but no entry was actually made as a result of this decision. Caterpillar's net income in $2020$ was $$2\mathrm{.}900$ million before recognition of any clean$-$up costs.

If needed adjustments were made to correct the error, what would be impact on the financial statements below:

a$)$ Change in Total Liabilities as of December $31,2020?$

b$)$ Change in Net Income for the Year Ended December $31,2020?$

c$)$ Briefly explain $($one sentence at most; two words are all that is necessary$),$ why Caterpillar had to make an entry after the board meeting, $($i$.$e$.,$ what conditions did it meet that required recognition$).$