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

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Built-in Mathematica Symbol

Equivalent

Equivalent[e₁, e₂, ...]
represents the logical equivalence

, giving True when all of the e_i are the same.

Equivalent[e₁, e₂, ...] can be input in StandardForm and InputForm as e₁e₂.... The character can be entered as Esc equiv Esc or \[Equivalent].

Test equivalence of Boolean expressions:

Enter using Esc eq Esc:

Test equivalence of Boolean expressions:

Enter using Esc eq Esc:

Automatic simplifications:

Prove equivalence between different Boolean expressions:

Use BooleanConvert to express Equivalent in terms of And and Or:

A well-known representation of two-argument Equivalent in terms of Implies:

This proves that the two representations are indeed equivalent:

Equivalent with two arguments is equivalent to Xnor:

For more arguments these are different primitives:

Use Resolve to prove equivalence of two systems of equations:

Equivalent is effectively Equal for Boolean expressions: