Problem: Consider the statements: (1) p∧q (2) p∧∼q(3)∼p∧q (4) ∼p∧∼q, where p and q are statements each of which may be true or false. How many of these imply the truth of ∼(p∧q)?
Answer Choices:
A. 0
B. 1
C. 2
D. 3
E. 4
Solution:
Form I. Since ∼(p∧q)=∼p∨∼q, statements (2),(3), and (4) are each correct.
Form II. The negation of the statement "p and q are both true" means that either p is true and q is false, or p is false and q is true, or p is false and q is false. Therefore, the statements (2).(3), and (4) are each correct.