Have to determine whether each one is true or false.

For #6. I used a similar proof for F(AUB). Had this:

suppose y∈(A⋂B)={F(x)|x∈A⋂B}

Then y=F(x) for some x∈A⋂B

y=F(x) where x∈A or x∈B

But x∈A---> y=F(x)∈F(A)

and x∈B--> y=F(x)∈F(B)

y∈F(A) and y∈F(B)

y∈F(A)⋂F(B)

is this correct or is this different way for ⋂?