Being a tautological consequent means, if all the statements are true, then R must be true. So, if P1, ... , Pn, P are true, so is R. Also, if P1, ... , Pn, Q are true, so is R. Note that the difference in the list of statements is P and Q. So if P *or* Q is one of the statements, then R is true. It follows that the statement R is true if P or Q is listed with the statements P1, ... , Pn as being true. You can use laws of inference to deduce this. Like the law of simplification, etc.

Gino T.

asked • 11/23/15# if R is a tautological consequence of P1, . . . ,Pn,P and also a tautological consequence of P1, . . . ,Pn,Q,

then R is a tautological consequence of P1, . . . ,Pn,P∨Q. Explain this please..i don't understand

How could you use the result established above to give a careful justification for adding

the Rule of ∨ - Elim to the system F?

the Rule of ∨ - Elim to the system F?

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Gino T.

the Rule of ∨ - Elim to the system F?

11/23/15