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Logic

  

Tautology

  

test for a tautology

  

Contradiction

  

test for a contradiction

 

Calling Sequence

Parameters

Description

Details

Examples

Calling Sequence

Tautology(b, p)

Contradiction(b, p)

Parameters

b

-

Boolean expression

p

-

(optional) unevaluated name

Description

• 

The Tautology and Contradiction commands test whether the given Boolean expression b is a tautology or a contradiction.

• 

The Tautology(b) calling sequence returns true if b is a tautology (true for every valuation of its variables) and false otherwise. Similarly, Contradiction(b) returns true if b is a contradiction (false for every valuation of its variables) and false otherwise.

• 

If the parameter p is supplied and the test returns false, then a valuation is assigned to p which demonstrates a negative result. Otherwise, p is assigned NULL. Note that the test may be significantly faster if p is not given.

Details

• 

The problem of determining whether every possible assignment of truth values satisfies a given Boolean formula is the dual of the the Boolean satisfiability problem and is known to be co-NP-complete, meaning that no polynomial-time algorithm is presently known.

Examples

withLogic:

Tautologya&andb&or&nota&or&notb

true

(1)

Tautologya&iffb&orb,p

false

(2)

p

a=true,b=false

(3)

Tautologya&or&nota,p

true

(4)

p

Contradictiona&or&nota&andb&norb

true

(5)

Contradictiona&iffb&orb,p

false

(6)

p

a=false,b=true

(7)

Contradiction&nota&anda,p

true

(8)

p

See Also

Logic

Logic/Equivalent

Logic/Satisfy