Which of the following statements about a binary tree is correct?(A) No binary tree is both complete and full(B) Every full binary tree is also a complete binary tree(C) Every complete binary tree is also a full binary tree(D) Every binary tree is either complete or full

The correct statement about a binary tree is (B) Every full binary tree is also a complete binary tree.

Here's why:

(A) No binary tree is both complete and full - This is incorrect. A binary tree can be both complete and full. A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible. A full binary tree is a binary tree in which every node has either 0 or 2 children. So, a binary tree can be both if it meets both conditions.

(B) Every full binary tree is also a complete binary tree - This is correct. If a binary tree is full, every level of the tree is fully filled, which also satisfies the condition of a complete binary tree.

(C) Every complete binary tree is also a full binary tree - This is incorrect. A complete binary tree can have nodes with only one child, which does not meet the condition of a full binary tree.

(D) Every binary tree is either complete or full - This is incorrect. A binary tree can be neither complete nor full. For example, a binary tree with 3 nodes and only left children is neither complete nor full.