Final answer:
The question seeks a logical equivalent to ~p → q, but the given options seem to have typographical errors and do not accurately represent logical statements. The correct logic equivalent is p ∨ q. In a probability context, two events are mutually exclusive if P(G AND E) is zero, which can be numerically validated.
Step-by-step explanation:
The question asks which statement is logically equivalent to the conditional statement ~p → q. The symbols used in the question options do not accurately represent logical statements or mathematical notations typically used in this context, which might be due to typographical errors. However, the concept of logical equivalence refers to two statements that are always logically equivalent, meaning they have the same truth values in every possible scenario.
To find an equivalent statement to ~p → q, we can use logical equivalences. The statement ~p → q is equivalent to p ∨ q (where ∨ represents the logical OR), because if ~p is false, then q must be true for the implication to hold. Without the context of properly formatted logical statements, none of the given options a) through e) represent logical expressions or an equivalent to the given conditional statement.
If we were to consider the logical equivalence in terms of probabilities (which notation hints at but is out of context for this question), we might express the equivalent as P(G OR E) for two events G and E. In probability, two events are considered mutually exclusive if they cannot both occur at the same time, which means P(G AND E) would be zero. The condition for mutual exclusivity can be checked numerically by assessing if the sum of the individual probabilities equals the probability of their union: P(G) + P(E) = P(G OR E).