Suppose the conclusion of an argument is logically equivalent to the conjunction of all the argument’s premises

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Suppose the conclusion of an argument is logically equivalent to the conjunction of all the argument’s premises (the conjunction of all the arguments premises is just the statement obtained by taking each premise singly and conjoining them all with the “and” operator to form one large statement). Do you have to do a truth table to know whether it is valid or invalid?

user14373

Posted 2015-04-21T00:18:54.420

Reputation: 63

Answers

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No, you don't need to do a truth table, and the argument is valid.

Again, the definition of validity is that an argument is valid if it is not possible for the premise to be false if all of the conclusions are true.

In the case you are describing, if the premises are false, then the conclusion is false, and if the premises are true, then the conclusion is true. Thus, no need for a truth table since no case could exist where there are true premises and a false conclusion.

virmaior

Posted 2015-04-21T00:18:54.420

Reputation: 23 970