Answer to Question #234709 in Discrete Mathematics for smi

Question

Q#: A binary operation ∇ on [0,1] is a t-norm if and only if x∇(y∇z)=(x∇y)∇z

Answer 1

∇ is t-norm <=> x∇(y∇z) =(x∇y)∇z

∇ is t-norm on [0,1]

∇ is associative

x,y,z $\in$ [0,1]

(x∇y)∇z = x∇(y∇z), $\forall$ x,y,z $\in$ [0,1]