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A detailed tutorial on identifying contradictions. Step by step tutorial including several examples of how to identify contradictions for reference.

A contradiction is a statement of only false values – one that is false no matter how you look at it. In terms of mathematical logic, it is defined as a propositional form that is false for every assignment of truth values to its components. In order for a statement to be a contradiction, when the proposition is on a truth table it must be false for every possible combination of P and Q.

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A detailed tutorial on identifying tautologies. Step by step tutorial including several examples of how to identify tautologies for reference.

A tautology is a statement of truth – one that is true no matter how you look at it. In terms of mathematical logic, it is defined as a propositional form that is true for every assignment of truth values to its components. In order for a statement to be a tautology, when the proposition is on a truth table it must be true for every possible combination of P and Q.

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A detailed tutorial of De Morgan’s laws. Step by step tutorial including several examples of De Morgan’s laws for reference.

De Morgan’s laws refer to the logical process of conjunction and disjunction, more commonly known as “and” and “or”. It deals with the negation of entire statements instead of just parts of a statement. De Morgan’s laws state that:

Not (P and Q) = (Not P) or (Not Q)

Not (P or Q) = (Not P) and (Not Q)

In the past, this has been referred to as “complete negation”. It is impossible to solve negations of logical operators without using De Morgan’s laws.