I'm taking an intro course in Lambda calculus and I cannot understand why in the following exercise, the first two sentences are false and only the last one is true:
λx.x β λx.x: False
λx.x -β λx.x: False
λx.x --β λx.x: True (beta-reduction closed under transitivity and reflexivity)
I thought that in an identity function, there should be no difference between beta-equivalence, beta-reduction and transitive and reflexive beta-reduction