Name: Section: Time: $30$ Minutes Full Marks: $20$ Determine whether the following PL formula is Satisfiable, Contradictory or Valid: $($p$^(^())$q$)->$rvvnotq In the game tree below, it is Max's turn to move. Inside each leaf node is the estimated score of that resulting position as returned by the heuristic static evaluator. i$.$ Perform Mini$-$Max search and label each branch node with its value. ii$.$ Cross out each leaf node that would be pruned by alpha$-$beta pruning Suppose a genetic algorithm uses chromosomes of the form x$=$abcdefg with a fixed length of eight genes. Each gene can be any digit between $0$ and $9.$ Let the fitness of individual x be calculated as: f$($x$)=($a$+$b$)-($c$+$d$)+($e$+$f$)-($g$+$h$),$ and let the initial population consist of four individuals with the following c