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.