None of these are taken.
Can I shorten this above speech like below:
Is this process grammatically right? If it is right then what are the rules behind it?
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"None taken" is actually used to reassure someone that they took no offense to something that was said in their previous statement. For example:
Person A: "That sweater is ugly. No offense, though."
Person B: "None taken."
So, the former will be the best option. However, you may want to specify what is being referred to by the pronoun these.