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In logic, statements p and q are logically equivalent if they have the same logical content. This is a semantic concept; two statements are equivalent if they have the same truth value in every model (Mendelson 1979:56). The logical equivalence of p and q is sometimes expressed as , E''pq'', or . However, these symbols are also used for material equivalence; the proper interpretation depends on the context. Logical equivalence is different from material equivalence, although the two concepts are closely related. ==Logical equivalences== Logical equivalences involving conditional statements： :#p→q≡¬p∨q :#p→q≡¬q→¬p :#p∨q≡¬p→q :#p∧q≡¬(p→¬q) :#¬(p→q)≡p∧¬q :#(p→q)∧(p→r)≡p→(q∧r) :#(p→q)∨(p→r)≡p→(q∨r) :#(p→r)∧(q→r)≡(p∨q)→r :#(p→r)∨(q→r)≡(p∧q)→r Logical equivalences involving biconditionals： :#p↔q≡(p→q)∧(q→p) :#p↔q≡¬p↔¬q :#p↔q≡(p∧q)∨(¬p∧¬q) :#¬(p↔q)≡p↔¬q 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「logical equivalence」の詳細全文を読む スポンサード リンク
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