Nonequivalent

If 👁 A=>!B
and 👁 B=>!A
(i.e., 👁 (A=>!B) ^ (B=>!A)
, where 👁 !A
denotes NOT, 👁 =>
denotes implies, and 👁 ^
denotes AND), then 👁 A
and 👁 B
are said to be inequivalent, a relationship which is written symbolically as 👁 A≢B
, 👁 A<=>AdjustmentBox[/, BoxMargins -> {{-1.05, 0.13913}, {-0.5, 0.5}}]B
, or 👁 A<->AdjustmentBox[/, BoxMargins -> {{-1, 0.13913}, {-0.5, 0.5}}]B
. Nonequivalence is implemented in the Wolfram Language as [A, B, ...]. Binary nonequivalence has the same truth table as XOR (i.e., exclusive disjunction), reproduced below.

See also

Connective, Equivalent, Exclusive Disjunction, XOR

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Cite this as:

Weisstein, Eric W. "Nonequivalent." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Nonequivalent.html

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