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Q: Are two tautologies consistent statements
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Are the two statements you don't always work on Tuesdays and you never work on Tuesdays logically consistent?

No.


Which of the following statements is consistent with the assertion that protists are paraphyletic?

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What is the consistent equation in mathematics?

Consistent equations are two or more equations that have the same solution.


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Tautologies are always true.


In a two-column proofthe first column states your reasons for the corresponding statements in the second column?

A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column.


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Does every statement have a counterexample?

No. Not if it is a true statement. Identities and tautologies cannot have a counterexample.


What does it mean for a system to be consistent or inconsistent?

does it stay the same or not? Actually, a system is inconsistent if you can derive two (or more) statements within the system which are contradictory. Otherwise it is consistent. For example, Eucliadean geometry requires that given a line and a point not on that line, you can have one and only one line through the point which is parallel to the original line. However, you can have a consistent system of geometry if you assume that there is no such parallel line. This is known as the projective plane. You can assume that there will be an infinite number of parallel lines through a point not on the line. And again you can have a consistent system. Consistency or inconsistency has nothing whatsoever to do with time.