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Mathematical Proof: Is the Argument Valid?

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Determine whether the following argument is valid:

P > Q
(~P & R) > S
~Q
:. ~R v S.

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Solution Summary

A detailed review of the meanings of the individual assumptions in the argument is provided. Then, to determine whether the argument is valid, the consequences of combining those assumptions are investigated.

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Statement 1 (P > Q) means "P implies Q."

Recall that an implication "X > Y" is true if and only if "~X v Y" is true (that is, if and only if X is false or Y is true (or both)).

Thus statement 1 is true if and only if P is false or Q is true (or both).

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Statement 2 [(~P & R) ...

Solution provided by:
Georgia Martin, PhD
Education
  • AB, Hood College
  • PhD, The Catholic University of America
  • PhD, The University of Maryland at College Park
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