1. We walk or run wearing these shoes.

(What is the part of speech of 'wearing' here? Is "wearing" a complement? Or is #1 come from #2 or #3 below?)

2. We walk or run as we wear these shoes.

3. We walk or run while we wear these shoes.

(Are the three all the same?)

1. wearing is a gerund, used here as an adjective.

Essentially the 3 sentences convey the same message: a) we wear, do wear, are wearing these shoes and b) we walk, do walk and are walking or run, do run, are running.

Sra

In sentence #1, "wearing" is the present participle form of the verb "wear" and functions as an adverbial phrase modifying the verb "walk or run." It describes the action of walking or running and indicates the manner in which it is done. It does not function as a complement in this sentence.

Sentences #2 and #3 have a similar meaning but differ slightly in their structure and emphasis. In both #2 and #3, "as" and "while" are conjunctions that indicate the simultaneous occurrence of two actions: walking/running and wearing shoes. In these sentences, "wear" is a finite verb and the main action, while "walk or run" is a subordinate clause that describes the concurrent action.

So, sentence #1 is slightly different from #2 and #3 in terms of grammatical structure, but they all convey the same meaning: that we walk or run while wearing the shoes.