PLEASE HELP ME. kindly show all your work 3. Let n ∈ N \ {0}. Describe the largest set of values n for which you think 2n < n!. Use induction toprove that your description is correct.Here m! stands for m factorial, the product of first m positive integers. 4. Prove that log2 n! ∈ O(n log2 n). Thank you. But please show all work and all steps

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Types of trees

A tree data structure is a non–linear structure that stores data hierarchically. It can be defined as a group of objects, called nodes. The nodes are linked with edges. Trees begin with a root node which leads to children nodes. The last children nodes (endpoints) are called leaf nodes, and they do not have children nodes.