I'm doing textbook homework for discrete mathematics and I'm struggling to understand how to solve the following practice problem. I would understand if they gave me variables and asked me to use premises to construct a specific argument, but I don't understand how to reduce it just to a value of false? Any help or hints would be appreciated.
Question:
Using only the rules of inference and the logical equivalences, show that the following argument is a contradiction by reducing it to a value of "False". You may assume that all the premises given are true.
𝑎 → 𝑏
¬𝑏 ∧ 𝑐
¬𝑎 → 𝑑
𝑑 → ¬𝑒
𝑒 ∧ f