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Z is needed for Y translates to:

  1. If Y ---> Z

  2. If Z ---> Y

  3. If Z --> ~Y

  4. If ~Y --> Z

The correct answer is: If Y ---> Z

When we say "Z is needed for Y," it means that in order for Y to occur or be true, Z must also occur or be true. This relationship can be represented as "If Y, then Z" (Y --> Z), which is the statement that corresponds to the given expression. This shows that Z is a necessary condition for Y to happen, hence the correct answer is A. Option B states "If Z, then Y," which would mean that Z is sufficient for Y, which is not what the original statement conveys. Option C states "If Z, then not Y," which is the contrapositive of the original statement. Option D states "If not Y, then Z," which is the inverse of the original statement. These do not accurately represent the relationship between Z and Y in the original statement.