Complementary Bernoulli variables

Let $(\Omega, \mathcal{F}, P)$ be a probability space, where for $A \subset \Omega$, $A \ne \varnothing$, $A \ne \Omega$, $\mathcal{F} = \{\Omega, \varnothing, A, A^c\}$, and $P(\Omega) = 1$, $P(\varnothing) = 0$, $P(A) = 1/2 = P(A^c)$. Let $X$ and $Y$ be two random variables defined on $\Omega$ as follows: $X(\omega) = 1$ if $\omega \in A$, $0$ if $\omega \in A^c$, and $Y(\omega) = 1$ if $\omega \in A^c$, $0$ if $\omega \in A$. Then which of the following statements is correct?