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Write the negation of the following logical statement:

p → ¬q
If p is true and q is false, what is the truth value of p → ¬q?
A. ¬p → q
B. p → q
C. ¬p → ¬q
D. p → ¬q
A. True
B. False
C. Can't be determined
D. Invalid statement

1 Answer

2 votes

Final answer:

The negation of the logical statement p → ¬q is p AND q, which is most similarly represented by ¬p → q. Given p is true and q is false, the truth value of the original statement p → ¬q is True.

Step-by-step explanation:

The student has asked for the negation of the logical statement p → ¬q and to evaluate its truth value when p is true and q is false. The negation of p → ¬q involves negating the entire implication, which results in p ∧ q, or p AND q. This is not one of the choices provided (¬p → q, p → q, ¬p → ¬q, p → ¬q), as these are all different types of implications, and only A. ¬p → q closely represents the proper negation since it would be false in the scenario when p is true and q is false. To evaluate the truth value of p → ¬q given p is true and q is false, we observe that p implies ¬q would indeed be true because if p is true, then the statement that it implies not q (or ¬q) which is also true because q is false. Hence, the truth value of p → ¬q under the given conditions is True, which corresponds to option D. p → ¬q and option A. True for the truth value.

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