A feckless tree is a 3-ary rooted tree where nodes are labeled with pairs of integers and that satisfies the following properties: a) If n is a leaf, then n is labeled (4,7) or (7,12) bj No internal node has exactly two children c) If an internal node n has one child labeled (p,q), then n is labeled (p+3,q+5) d) If an internal node n has three children labeled (p.q). (r.s) and (tu), then n is labeled (2(p+r+t)+1, 2(q+stu)). Prove that in any feckless tree, if the root is labeled (p.q), then 3q 5p+1 A feckless tree is a 3-ary rooted tree where nodes are labeled with pairs of integers and that satisfies the following properties: a) If n is a leaf, then n is labeled (4,7) or (7,12) bj No internal node has exactly two children c) If an internal node n has one child labeled (p,q), then n is labeled (p+3,q+5) d) If an internal node n has three children labeled (p.q). (r.s) and (tu), then n is labeled (2(p+r+t)+1, 2(q+stu)). Prove that in any feckless tree, if the root is labeled (p.q), then 3q 5p+1