p → q is logically equivalent to ¬p ∧ q¬p ∨ q¬p ∨ ¬qp ∨ ¬q
Question
p → q is logically equivalent to ¬p ∧ q¬p ∨ q¬p ∨ ¬qp ∨ ¬q
Solution
The statement seems to be a mix of different logical equivalences. Let's break it down:
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"p → q" is a logical implication which means "if p then q".
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"¬p ∧ q" is a logical conjunction which means "not p and q".
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"¬p ∨ q" is a logical disjunction which means "not p or q".
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"¬p ∨ ¬q" is another logical disjunction which means "not p or not q".
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"p ∨ ¬q" is another logical disjunction which means "p or not q".
However, these are not all logically equivalent. The correct logical equivalence for "p → q" is "¬p ∨ q", which means "if p then q" is logically equivalent to "not p or q". The other statements are not logically equivalent to "p → q".
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