Is P(A≤−B)= 1− P(A≤B) an correct equation?

Question

Is P(A≤−B)= 1− P(A≤B) an correct equation? If yes, kindly provide the derivation of the same.

As I get it, P(A≤−B)= 1− P(A>−B) i.e. 1−P(−A

Answer 1

If $B$ is positive and $A =2B$ then $P(A \leq -B)=0$ and $ 1-P(A \leq B)=1-0=1$. The event $(A \leq -B)$ is not the complement of the event $(A \leq B)$. If $E$ and $F$ are complementary events then $P(E)=1-P(F)$ but we don't have complementary events here.