I have been doing a homework assignment wherein I have been trying to determine the result of ((or true) false) using beta reduction. I began by writing the entire expression using lambda notation and performed the following steps:
((λx.λy.((x (λa.λb.a)) y) (λa.λb.a)) (λa.λb.b)) ((λx.(x (λa.λb.a)) (λa.λb.a) ) (λa.λb.b)) (((λa.λb.a) (λa.λb.a))) (λa.λb.b)) ((true true) false)
I don't understand how to go about simplifying this further, however. Can someone explain whether this is the final result, or what further steps I can take? I'm just learning lambda calculus, and haven't quite gotten a feel for it yet.