Question

For transformations Z, Y, W, if Y∘W=I, then Y∘W∘Z=Z. True or false?

a) True
b) False

Answer 1

The composition of transformations Y, W, and Z equals Z.

Step-by-step explanation:

The statement Y∘W=I means that the composition of transformations Y and W equals the identity transformation, I. If Y∘W∘Z=Z, it means that the composition of transformations Y, W, and Z equals Z.

Let's analyze this statement:

1. If Y∘W=I, then Y∘W∘Z=Y∘W∘Z∘I (since I is the identity transformation).
2. We can rearrange the expression as (Y∘W)∘Z=(Y∘W)∘Z∘I.
3. From the associativity of compositions, we have Y∘(W∘Z)=Y∘(W∘Z∘I).
4. Since (W∘Z∘I) becomes Z, the expression simplifies to Y∘Z=Y∘Z.
5. This means that Y∘W∘Z=Z is true.

Therefore, the answer is a) True.