Final answer:
The statement Y∘W=I thus Y∘W∘Z=Z is false because it incorrectly assumes that function composition is commutative, which is not generally the case in mathematics.
Step-by-step explanation:
For transformations Z, Y, W, the statement if Y∘W=I (where I is the identity transformation), then Y∘W∘Z=Z is actually false. This is because function composition is not generally commutative; the order in which functions are applied matters. The identity transformation I maintains an element unchanged when composed with any other transformation. However, stating Y∘W∘Z=Z assumes that Z remains unchanged after the application of Y and W, which is only the case if Z is the identity or commutes with Y and W, which is not generally true.