Question

9. Give a recursive definition of one of the following: (a) the set $Z^+$ of positive integers (b) the set $RB$ of rooted binary trees. 10. How many relations are possible on a set with 10 elements, if the relations must be both reflexive and symmetric? (Hint: consider the possible 0 \textendash{} 1 matrices representing such relations.) 11. (a) How many leaves does a full binary tree with 55 internal vertices have? (b) What is the height of a full, balanced 3-ary tree with 96 leaves? 12. Use the Handshaking Theorem to prove or disprove the following statement: there exists a simple graph with 12 vertices of degree 2, 6 vertices of degree 3, and 20 edges. 13. Construct a binary search tree to store the following list of chemical symbols: Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn

          9. Give a recursive definition of one of the following:
(a) the set $Z^+$ of positive integers
(b) the set $RB$ of rooted binary trees.
10. How many relations are possible on a set with 10 elements, if the relations must be both reflexive
and symmetric? (Hint: consider the possible 0 \textendash{} 1 matrices representing such relations.)
11. (a) How many leaves does a full binary tree with 55 internal vertices have?
(b) What is the height of a full, balanced 3-ary tree with 96 leaves?
12. Use the Handshaking Theorem to prove or disprove the following statement: there exists a simple
graph with 12 vertices of degree 2, 6 vertices of degree 3, and 20 edges.
13. Construct a binary search tree to store the following list of chemical symbols:
Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn

9. Give a recursive definition of one of the following:
(a) the set Z^+ of positive integers
(b) the set RB of rooted binary trees.
10. How many relations are possible on a set with 10 elements, if the relations must be both reflexive
and symmetric? (Hint: consider the possible 0 – 1 matrices representing such relations.)
11. (a) How many leaves does a full binary tree with 55 internal vertices have?
(b) What is the height of a full, balanced 3-ary tree with 96 leaves?
12. Use the Handshaking Theorem to prove or disprove the following statement: there exists a simple
graph with 12 vertices of degree 2, 6 vertices of degree 3, and 20 edges.
13. Construct a binary search tree to store the following list of chemical symbols:
Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn

Added by Angelica M.

Question

Please give Ace some feedback