Logical Equivalence

In mathematics, two statements are logically equivalent if they produce the same truth value in every case. For example, "x is greater than 7" and "x is not less than or equal to 7" are logically equivalent because they are both true or both false simultaneously for every real number x. A conditional ($P/impliesQ$) and its contrapositive ($\neg Q/implies\neg P$) are always logically equivalent. For example, "if x is even, then x is divisible by 2" is logically equivalent to its contrapositive, "if x is not divisible by 2, then x is not even".

Resources

• Logical Equivalence, Wikipedia
• Logical Equivalences, Mathematics LibreTexts
• Logical Equivalence and Truth Tables, United States Naval Academy College of Mathematics