test for a tautology
test for a contradiction
(optional) unevaluated name
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.
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.
Tautology⁡a &and b &or `¬`⁡a &or `¬`⁡b
Tautology⁡a &iff b &or b,'p'
Tautology⁡a &or `¬`⁡a,'p'
Contradiction⁡a &or `¬`⁡a &and b &nor b
Contradiction⁡a &iff b &or b,'p'
Contradiction⁡`¬`⁡a &and a,'p'
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