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The type of syllogism being used in the given sentence is a conditional syllogism.
This refers to the use of reasoning in order to draw conclusions about something based on two premises.
Hence, we can see that conditional syllogism was used in the given premises and this is because it made use of either-or to show that if the sidewalk was wet, then that means that it must have rained.
This reasoning is faulty because there are different possible reasons for the sidewalk to be wet and not just rainfall.
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