Final answer:
The proposition that is logically equivalent to ¬p→ q is 'p or q', denoted as 'p V q'. This means that if 'not p' is true, then 'q' must also be true, otherwise 'p' itself is true. Therefore, option (b) 'p V q' is the correct answer.
Step-by-step explanation:
To explain the proposition that is logically equivalent to ¬p→ q, we must first understand the meaning of the logical symbols. The symbol ¬ denotes negation, and → represents a conditional, meaning 'if ... then ...'. In logical terms, the conditional ¬p→ q can be read as 'if not p, then q', which is logically equivalent to either p is true or q is true. Therefore, the equivalent proposition is 'p or q'.
In terms of the answer choices provided, the notation 'p V q' represents the logical 'or', which makes option (b) 'p V q' the correct logically equivalent proposition to ¬p→ q. The other options represent conjunction (p ^ q) or the logical 'and', which is not equivalent to the conditional statement we are analyzing.