p^~q write the negation
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The negation of p ∧ q asserts “it is not the case that p and q are both true”. Thus, ¬(p ∧ q) is true exactly when one or both of p and q is false, that is, when ¬p ∨ ¬q is true. Similarly, ¬(p ∨ q) can be seen to the same as ¬p ∧ ¬q. ... The statement is false only when p is true and q is false
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