• You are expected to use mathematical notation to solve this problem, not pseudocode or a programming language.

Consider list A = (W.1, y, z), deployed to implement a Queue Abstract Data Type. 1. Let the head of A correspond to the front position of the Queue. Implement operations enqueue (el, A) and dequeue (A) using list construction operations. In both cases we can refer to l' as the state of the list upon successful termination of one of its operations. 2. Let us now reverse the way we manipulate our data structure and let the head of A correspond to the rear of the Queue. (a) What would be the result of cons(el. A), and would it be a correct implementation for operation enqueue (el, A)? (b) What would be the result of list(el. A), and would it be a correct implementation for operation enqueue (el, A)? (c) What would be the result of concat(list(el), A), and would it be a correct imple- mentation for operation enqueue (el, A)? Consider list A = (W.1, y, z), deployed to implement a Queue Abstract Data Type. 1. Let the head of A correspond to the front position of the Queue. Implement operations enqueue (el, A) and dequeue (A) using list construction operations. In both cases we can refer to l' as the state of the list upon successful termination of one of its operations. 2. Let us now reverse the way we manipulate our data structure and let the head of A correspond to the rear of the Queue. (a) What would be the result of cons(el. A), and would it be a correct implementation for operation enqueue (el, A)? (b) What would be the result of list(el. A), and would it be a correct implementation for operation enqueue (el, A)? (c) What would be the result of concat(list(el), A), and would it be a correct imple- mentation for operation enqueue (el, A)