Thread: Is f injective? Surjective? Bijective?

Let U be an universe, and V⊆U . Define a function f:P(U)→P(V), by f(A)=A∩V, for all A∈P(U). Is f injective? Surjective? Bijective? Fully justify your answers.

Not really sure where to start with this one. I would think its injective since, if I let f(A)=f(B) then A∩V=B∩V. This would mean B=A. But, I think I would have to do cases, because B can't always be equal to A....? I'm not sure what I'm doing.

Some help would be appreciated.

Originally Posted by Danneedshelp

Let U be an universe, and V⊆U . Define a function f:P(U)→P(V), by f(A)=A∩V, for all A∈P(U). Is f injective? Surjective? Bijective? I would think its injective since, if I let f(A)=f(B) then A∩V=B∩V. This would mean B=A. But, I think I would have to do cases, because B can't always be equal to A....? .

If does not necessarily imply that .

Because then .
Does that show that is surjective?