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The question is not complete.

That's the diagram for the implementation of the output Z.

But since, I don't do this course I can't be sure of my answer.

use map method to solve it ans is A' +B'C'

how to design a mosfet

Sorry again for not being of much help..!! :)

mosfet for what?

the question clearly stated to design a mosfet such that the output is exact as giveb below