Final answer:
The equivalent expression to ¬(p→q) is 'p AND not q', which in logical notation is p∧¬q. The correct answer is thus option c, which correctly represents this logical relationship.
Step-by-step explanation:
The logical expression ¬(p→q) can be translated to 'not (if p then q)', which means 'if p occurs, then q does not occur'. The conditional p→q is true in all cases except when p is true and q is false. Therefore, the negation ¬(p→q) is equivalent to p being true and q being false, which is 'p AND not q', or in logical notation, p∧¬q.
Let’s go through the options provided:
- a. p∨¬q: This represents 'p OR not q', which is not equivalent.
- b.¬p→¬q: This means 'if not p then not q', which is also not equivalent.
- c. p∧¬q: This is 'p AND not q', which is the correct equivalence to ¬(p→q).
- d. q→p: This is 'if q then p', which is not the equivalent we are looking for.
The correct answer is c. p∧¬q.