$$P\left( {A/B} \right) \ge {{P\left( A \right) + P\left( B \right) - 1} \over {P\left( B \right)}},P\left( B \right) \ne 0$$ is always true

$$P\left( {A \cap \overline B } \right) = P\left( A \right) - P\left( {A \cap B} \right)\,\,$$ does not hold

$$P\left( {A \cup B} \right) = 1 - P\left( {\overline A } \right)P\left( {\overline B } \right),$$ if $$A$$ and $$B$$ are independent

$$P\left( {A \cup B} \right) = 1 - P\left( {\overline A } \right)P\left( {\overline B } \right),$$ if $$A$$ and $$B$$ are disjoint.

$$E$$ and $$F$$ are mutually exclusive

$$E$$ and $${F^c}$$ (the complement of the event $$F$$) are independent

$${E^c}$$ and $${F^c}$$ are independent

$$P\left( {E|F} \right) + P\left( {{E^c}|F} \right) = 1.$$

not less than $$P\left( A \right) + P\left( B \right) - 1$$

not greater than $$P\left( A \right) + P\left( B \right)$$

equal to $$P\left( A \right) + P\left( B \right) - P\left( {A \cup B} \right)\,\,$$

$$P\left( A \right) + P\left( B \right) + P\left( {A \cup B} \right)\,\,$$

$$P\left( M \right) + P\left( N \right) - 2P\left( {M \cap N} \right)$$

$$P\left( M \right) + P\left( N \right) - P\left( {M \cap N} \right)$$

$$P\left( {{M^c}} \right) + P\left( {{N^c}} \right) - 2P\left( {{M^c} \cap {N^c}} \right)$$

$$P\left( {M \cap {N^c}} \right) + P\left( {{M^c} \cap N} \right)$$