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😃: Useresolution to show that the hypotheses “It is not rain
ing or Yvette has her umbrella,” “Yvette does not have
her umbrella or she does not get wet,” and “It is raining
or Yvette does not get wet” imply that “Yvette does not
get wet.”
🤖: Sure! Here's a proof of the resolution you provided:
Let H1 be "It is not raining or Yvette has her umbrella," H2 be "Yvette does not have her umbrella or she does not get wet," and H3 be "It is raining or Yvette does not get wet." We want to show that if any of these hypotheses are true, then Yvette will not get wet.
First, suppose H1 is true. Then, by hypothesis, either it is raining (and therefore Yvette does not get wet) or Yvette has her umbrella (and therefore Yvette will not get wet).
Next, suppose H2 is true. Then, by hypothesis, either Yvette does not have her umbrella (and therefore Yvette gets wet) or Yvette gets wet (and therefore Yvette does not have her umbrella). In both cases, we have shown that Yvette will get wet, which contradicts H2. Therefore, H2 cannot be true.
Finally, suppose H3 is true. Then, by hypothesis, either it is raining (and theref...