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The question of whether a solution to a given problem exists. The existence problem can be solved in the affirmative without actually finding a solution to the original ...

A disjunction that remains true if either or both of its arguments are true. This is equivalent to the OR connective. By contrast, the exclusive disjunction is true if only ...

A formal theory is said to be incomplete if it contains fewer theorems than would be possible while still retaining consistency.

A set of maximum degree to which all other degrees of recursively enumerable sets can be many-one reduced. If set A is many-one complete, then it is one-one complete, and ...

The operation of interchanging true and false in a logical statement. The negation of A is often called "NOT-A," and can be denoted !A, or with the negation sign ¬, so not-A ...

If A=>!B and B=>!A (i.e., (A=>!B) ^ (B=>!A), where !A denotes NOT, => denotes implies, and ^ denotes AND), then A and B are said to be inequivalent, a relationship which is ...

A set of maximum degree to which all other degrees of recursively enumerable sets can be one-one reduced. If set A is many-one complete, then it is one-one complete, and vice ...

You buy 100 pounds of potatoes and are told that they are 99% water. After leaving them outside, you discover that they are now 98% water. The weight of the dehydrated ...

Deciding whether a given Boolean formula in conjunctive normal form has an assignment that makes the formula "true." In 1971, Cook showed that the problem is NP-complete.

Socrates is reported to have stated: "One thing I know is that I know nothing."