Equivalent

Equivalent[e1,e2,]

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

Details

Examples

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Basic Examples  (2)

Test equivalence of Boolean expressions:

Enter using equiv:

Scope  (2)

Automatic simplifications:

TraditionalForm formatting:

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:

Introduced in 2008
 (7.0)