The reverse inclusion $\displaystyle F(A)\cap F(B)\supseteq F(A\cap B)$ is not true.
ok i think i see what you mean now. the = in the problem means it's both ways. so i have proven one way which is true but the reverse inclusion is not true. so the answer for number 6 is NO.
now do i have to do the reverse inclusion for number 7 as well?