Discrete Mathematics || week 8 assignment solution || NPTEL

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This week's questions were really overwhelming.
please do tick these answers if you have not made yourself or are unable to make. i too have struggled with this week assignment. they are exponentially increasing the level of the questions. some of these were research level questions, so I've done my best in solving them. one definitely need more practice before attempting these questions what I belive.
till then, it's math o'clock. happy math making.
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I'm not sure of 1 and 7, if someone have the solutions, kindly drop it here.

kunalkumar