In a full binary tree if number of internal nodes is I, then number of leaves L are?OptionsL = 2*IL = I + 1 L = I – 1L = 2*I – 1

To find the relationship between the number of internal nodes $I$ and the number of leaves $L$ in a full binary tree, we can break down the problem as follows:

1. Break Down the Problem

We need to derive the number of leaves $L$ based on the internal nodes $I$ in a full binary tree. A full binary tree is defined such that every internal node has exactly two children.

2. Relevant Concepts

In a full binary tree:

• The number of leaves $L$ can be expressed in terms of the number of internal nodes $I$.
• A fundamental property of full binary trees is that the number of leaves can be calculated using the formula: $L = I + 1$

3. Analysis and Detail

Given that:

1. Each internal node has two children,
2. The total number of nodes in the tree $N$ can be expressed as the sum of internal nodes and leaves: $N = I + L$
3. For every full binary tree, the relationship between the internal nodes and leaves leads us to the formula: $L = I + 1$ This formula emerges from the fact that each internal node contributes one more leaf than the number of internal nodes themselves.

4. Verify and Summarize

If $I$ is the number of internal nodes, then calculating $L$ using the formula $L = I + 1$ holds true for all full binary trees.

Final Answer

Thus, the correct relationship between the number of internal nodes $I$ and the number of leaves $L$ is: $L = I + 1$ So the answer is the second option: $L = I + 1$.