Alice and Bob play a game. Each secretly chooses a positive rational number in lowest terms. ( Alice ' s numberis a / x and Bob ' s is b / y ) . They reveal the numbers and add them ( forming ay bx / xy ) . Alice wins if the sum is notimmediately in lowest terms. ( For instance, if they choose 1 / 3 and 1 / 4 , the sum is 7 / 1 2 which is in lowest terms, leading to a win for Bob. But if they choose 1 / 6 and 4 / 3 , the sum is 2 7 / 1 8 , which is not in lowest terms, and Alice wins. ) The perfect strategy for this game may require number theory, which neither player has fully learned yet, but theyare familiar with properties of odd and even numbers. We can classify rational numbers in lowest terms as one ofthree kinds: oddodd , oddeven , or evenodd . Which of these kinds of numbers should Alice choose to maximize her chancesof winning? Which kind of number should Bob choose to prevent her from winning?Your solution should be thorough ( investigate