Final answer:
The weakest precondition for statement A is x > 3 and y > 9. The weakest precondition for statement B is x > 3 and y > 2.
Step-by-step explanation:
The weakest precondition for statement A, x = 2 * (y + 2*x); y=3*X-6 {y > 9}, is x > 3 and y > 9. To determine the weakest precondition, we need to analyze the requirements of the given statements. In this case, the condition {y > 9} implies that y must be greater than 9. The assignment statement x = 2 * (y + 2*x) and y = 3*x-6 don't impose any restrictions on y, so the weakest precondition is simply y > 9.
For statement B, if (x >y) y=6*x+ 2 else y= 3 * x+9; {y > 2}, the weakest precondition is x > 3 and y > 2. The condition {y > 2} implies that y must be greater than 2. The condition (x > y) in the if-else statement implies that x must be greater than y. Therefore, the weakest precondition is x > 3 and y > 2.