Consider two binary operators ‘$\uparrow$’ and ‘$\downarrow$’ with the precedence of operator $\downarrow$ being lower than that of the operator $\uparrow$. Operator $\uparrow$ is right associative while operator $\downarrow$ is left associative. Which one of the following represents the parse tree for expression $(7 \downarrow 3 \uparrow 4 \uparrow 3 \downarrow 2)$?

Given the expression: $7 \downarrow 3 \uparrow 4 \uparrow 3 \downarrow 2$

1. Precedence and Associativity Rules:

   • $\uparrow$ has higher precedence than $\downarrow$, and is right-associative.

   • $\downarrow$ has lower precedence, and is left-associative.

2. Parenthesization according to rules:

   • First, group the higher precedence operator $\uparrow$ from right to left:

     $$(3 \uparrow (4 \uparrow 3))$$

   • Next, group the lower precedence operator $\downarrow$ from left to right:

     $$((7 \downarrow (3 \uparrow (4 \uparrow 3))) \downarrow 2)$$

3. Constructing the Parse Tree:

   • The operator evaluated last is at the root: the second $\downarrow$.

   • Its left child represents $(7 \downarrow (3 \uparrow (4 \uparrow 3)))$ and its right child is $2$.

   • For the subtree $(7 \downarrow (3 \uparrow (4 \uparrow 3)))$, the root is $\downarrow$, with left child $7$ and right child $(3 \uparrow (4 \uparrow 3))$.

   • For the subtree $(3 \uparrow (4 \uparrow 3))$, the root is $\uparrow$, with left child $3$ and right child $(4 \uparrow 3)$.

   • For $(4 \uparrow 3)$, the root is $\uparrow$, with left child $4$ and right child $3$.

This structure corresponds exactly to tree (B).