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Mathematica > Mathematics and Algorithms > Discrete Mathematics > Boolean Computation >

Mathematica > Mathematics and Algorithms > Logic & Boolean Algebra > Boolean Computation >

Built-in Mathematica Symbol

Xnor

Xnor[e₁, e₂, ...]
is the logical XNOR (not XOR) function. It gives True if an even number of the

are True, and the rest are False. It gives False if an odd number of the

are True, and the rest are False.

Xnor[e₁, e₂, ...] can be input in StandardForm and InputForm as e_ie₂.... The character can be entered as Esc xnor Esc or \[Xnor].

Xnor gives symbolic results, applying various simplification rules automatically.

Unlike And, Nand, Or and Nor, Xnor must always test all its arguments, and so is not a control structure, and does not have attribute HoldAll.

Xnor in disjunctive normal form:

Enter using Esc xnor Esc:

Xnor in disjunctive normal form:

Enter using Esc xnor Esc:

Automatic simplifications:

Elimination of constants:

Xnor is commutitive and sorts its arguments:

Xnor in n varibles has a disjunctive normal form of length 2^n-1:

Xnor is equivalent to the negation of Xor:

For two variables Xnor is the same as Equivalent:

But they differ for more then two variables:

The 2D truth table for Xnor of 12 variables: