# Equivalent

Equivalent[e1,e2,]

represents the logical equivalence e1e2, giving True when all of the ei are the same.

# Details • Equivalent[e1,e2,] can be input in StandardForm and InputForm as e1e2. The character can be entered as equiv or \[Equivalent].
• As a Boolean function, Equivalent[e1,e2,] is equivalent to (e1e2)(¬e1¬e2).

# Examples

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## Basic Examples(2)

Test equivalence of Boolean expressions:

Enter using equiv :

## Scope(2)

Automatic simplifications:

## Applications(1)

Prove equivalence between different Boolean expressions:

## Properties & Relations(7)

Truth table for binary Equivalent:

Ternary Equivalent:

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 can be represented in terms of BooleanCountingFunction:

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: