Let and be sets , let and , and let be a projection map.

Show that .

I wonder if the question is correct. For example, let = {1, 2} and = {a,b}. Then, = {(1,a), (1,b), (2,a), (2,b)}.

Suppose and .

Suppose = {1} {1,2} = .

Then = {(2,b)} = {(1,a), (1,b)}.

Please check whether I am right that the proposition was wrong from the question.