Question

why do jain monks cover their mouth an nose with a cloth

Answer 1

Hi✌
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According to digamber jain scriptures , jain monks doesn't wear any cloths because they are vitragi and vitragi has no more liking left.

Not all Jain monks cover their faces with any mask. 

Monks belonging to one of the sect cover their mouth as they have a notion it would safeguard organisms present in Air.

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Hope it helps you✌

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Answer 2

Jain monks cover there mouth an nose with a cloth because they prefer to abide Non-violence.  They don't want to harm the tiny organisms which can be killed while talking. Secondly, while studying or investigating manuscripts and communicating with elders, they want to prevent spitting of saliva which can cause the symbol of disrespect.