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Say we are given the following statement

A ≡ B

where A is some logic statement and B is some logic statement. Determine if it is tautology, contingent or contradiction.

I know the definition of the three; tautology where the last column in truth table is all TRUE, contradiction where the last column in truth table is all FALSE and contingent where the last column in truth table is a mixed of TRUE and FALSE.

I can generate a truth table easily with A and B (given some logic statement). But when I get the final columns for A or B, how can I determine if it is tautology, contingent or contradiction? Assume the following scenario:

Scenario 1

Last column of A in the following sequence - T, T, F, T and last column of B in the following sequence - T, T, F, T. Is this a tautology because both last column matches and are equivalence?

Scenario 2

Last column of A in the following sequence - F, T, F, T and last column of B in the following sequence - T, T, F, T. Is this a contingent because both columns do not match exactly?

Scenario 3

Last column of A in the following sequence - F, F, T, F and last column of B in the following sequence - T, T, F, T. Is this contradiction because both columns are exactly the opposite?

Lastly, instead of using truth table, is it possible to apply the law of logic to solve such questions?

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  • $\begingroup$ You know the definitions, you know how build a t-t... but you have to put together the two :-) In the final column of the t-t you must have the formula $A \equiv B$: if all the rows have $T$, then the formula is a tautology. If all are $F$, it is a contradiction. $\endgroup$ May 5 '20 at 12:56
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All three of your scenarios are correct. But I'm not quite sure what you mean by "law of logic" -- though there might be shortcuts, in some sense the truth tables are the rules you will have to follow eventually to show whether a statement is a tautology, contradiction, or contingent.

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  • $\begingroup$ Hi there, thanks. By law of logic I meant laws such as DeMorgan's Law, Associative Law and so on. Any idea if it is right if I apply such laws on such question? $\endgroup$
    – SunnyBoiz
    May 5 '20 at 5:10

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