The probabilities that a student passes in Mathematics, Physics and Chemistry are $$m, p$$ and $$c,$$ respectively. Of these subjects, the student has a $$75%$$ chance of passing in at least one, a $$50$$% chance of passing in at least two, and a $$40$$% chance of passing in exactly two. Which of the following relations are true?

If $$\overline E $$ and $$\overline F $$ are the complementary events of events $$E$$ and $$F$$ respectively and if $$0 < P\left( F \right) < 1,$$ then

Let $$0 < P\left( A \right) < 1,0 < P\left( B \right) < 1$$ and
$$P\left( {A \cup B} \right) = P\left( A \right) + P\left( B \right) - P\left( A \right)P\left( B \right)$$ then

$$E$$ and $$F$$ are two independent events. The probability that both $$E$$ and $$F$$ happen is $$1/12$$ and the probability that neither $$E$$ nor $$F$$ happens is $$1/2.$$ Then,