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Question:

The proposition ¬p ∨ (p ∧ ¬q) is equivalent to:

p → ¬q

p ∨ ¬q

q → p

p ∧ ¬q

Solution:

¬p ∨ (p ∧ ¬q)

p | q | ¬p | ¬q | p ∧ ¬q | ¬p ∨ (p ∧ ¬q) | p → ¬q
T | T | F | F | F | F | F
T | F | F | T | T | T | T
F | T | T | F | F | T | T
F | F | T | T | F | T | T

The truth table shows that ¬p ∨ (p ∧ ¬q) is equivalent to p → ¬q.