Question: prove that NOR is a universal gate ( meaning: create AND, OR , NOT operations using only NOR gates ) Can you correct my errors

prove that NOR is a universal gate (meaning: create AND, OR , NOT operations using only NOR gates)Can you correct my errors based on these comments: For Not operation you need to take single input. Similarly, other circuits are not correct. Also, all combinations are not shown.
prove that NOR is a universal gate ( meaning:

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