26. True or false: the elements along the diagonal of an adjacency matrix representation of a graph correspond to self- edges, Le. edges of the form (aal where a ls a node in the graph. 27. If every node in a binary tree has two children except the leaf terminal) nodes, and the longest path in the graph from the root to a leaf has 3 edges, can there be 7 nodes in the graph? 28. A binary tree with n nodes were every leat node is exactly the same distance from the root. has how many nodes? 29. True or false. A graph without a spanning tree is not a connected graph 30. True or false, depth-frst search involves baktracking 31. Let A- (1.2.3.4), B-12.3.4.5.6), C- (6). What is(A Intersect B) union C? 32 The set xIx*2-2-0 and x is a real number) is empty 33 True or false: The intersection of the set of real numbers greater than 1 and the set described in problem 32 is empty 34. pv(a a where p - T.g E..T 35. The statements "if it is raining outside, it is cloudy" and 'either it is cloudy or it is not raining outside' are logically equivalent 36. To determine the truth or falsehood of the statement "There are other fish in the sea; where would you look? 37. The statement 'There is a non-blue fish and "Not all fish are blue' are logically equivalent