In the content of Alpha Beta pruning in game trees which of the following…

Final answer: The true statements are the one about pruning when a bound crossing occurs, the one about reducing computation, and the one about initializing bounds to negative and positive infinity. The claim that pruning guarantees the optimal solution by exploring the entire game tree is false.

• Pruning condition clarified: Alpha-Beta pruning can eliminate a subtree with certainty when the evaluated value causes a bound crossing (in practice this is when the current alpha becomes greater than or equal to beta). That means the remaining nodes in that subtree cannot affect the final minimax decision and can be skipped.

• Primary purpose: The main goal of Alpha-Beta pruning is to save computation by reducing the number of nodes searched while producing the same minimax result as an exhaustive search would.

• Incorrect claim explained: The statement that Alpha-Beta pruning guarantees the optimal solution by exploring the entire game tree is wrong. Alpha-Beta still guarantees the optimal minimax value, but it usually does so without exploring every node because it prunes branches that cannot affect the outcome.

• Initialization: At the root, initialize alpha = negative infinity and beta = positive infinity. These bounds are updated during the search and determine when pruning occurs.

Putting it together: the correct set of statements contains the pruning-condition statement (as clarified above), the purpose-of-pruning statement, and the initialization statement. The statement claiming that pruning guarantees the optimal solution by exploring the entire tree is false.