6.1 - 1:
Define n to be the number of elements in a heap of height h, then:
6.1-2:
6.1-3:
For any of the sub-tree of one max-heap, it maintains the basic heap property, i.e., A[parent(i)] >= A[i]. and the root of one sub-tree is the ancestor of all its nodes, therefore, the root is the largest by recurrence relation.
6.1-4:
The smallest element would be at the leaf of the heap, since its parent is larger that that heap.
6.1-5:
It's not. Example of a heap which is also a sorted array: 1, 2,3, 4,5,6,7
While Example which a heap is not: 1, 2,3, 6,5,4,7
6.1-6:
6.1-7:
(Proof by Mathematical Induction, it's also possible done by reasoning):
