Let G be an undirected graph. Consider a depth-first traversal of G, and let T be the resulting depth-first search tree. Let u be a vertex in G and let v be the first new (unvisited) vertex visited after visiting u in the traversal. Which of the following statements is always true?

Suppose you are given an array s[1..n] and a procedure reverse (s, i, j) which reverse the order of elements in s between positions i and j (both inclusive). What does the following sequence do, where $$1 \le k < n:$$ reverse (s, 1, k);
reverse (s, k+1, n);
reverse (s, 1, n);

Given relations r( w, x ) and s( y, z ), the result of

select distinct w,x
from r, s;

is guaranteed to be same as r, provided

In SQL, relations can contain null values, and comparisons with null values are treated as unknown. Suppose all comparisons with a null value are treated as false. Which of the following pairs is not equivalent?