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In the case of each of the following, decide whether or not the deduction is valid. If it is valid give a natural deduction proof;

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In the case of each of the following, decide whether or not the deduction is valid. If it is valid give a natural deduction proof; if not, provide a model in which it does not hold. Clearly label each step of the proof to indicate which rule is used at each stage. i. qrpqpr ii. xP(x)xP(x)

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