Use theorem 2.1.1 to verify the logical equivalences in 50–54. supply a reason for each step.

∼(p ∨ ∼q) ∨ (∼p ∧ ∼q) ≡ ∼p

The boiling point of water at an elevation of 0 feet is 212 degrees fahrenheit (°f). for every 1,000 feet of increase in elevation, the boiling point of water decreases by about 2°f. which of the following represents this relationship if b is the boiling point of water at an elevation of e thousand feet? a) e = 2b - 212 b) b = 2e - 212 c) e = -2b + 212 d) b = -2e + 212