ou are given a boolean expression consisting of a string of the symbols $$true$,$false$,$and$,$or$,$

and $$xor$.$ Count the number of ways to parenthesize the expression such that it will evaluate to

true. For example, consider the expression $$T or F xor T$($T and F represent true and false$).$

It can be parenthesized in two ways:

$(($T or F$)$ xor T$),$

$($T or $($F xor T$)),$

where only one of them $($the second parenthesization$)$ evaluates to true.

To solve this problem using dynamic programming, we define two $2-$D arrays, T and F $,$ that represent

the number of ways the expression can be parenthesized so that it evaluates to true or false,

respectively.

$($a$)[10$ points$]$ Find all different parenthesizations of $$F and T xor T or F and F$$ that evaluate

to true.

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Question $4$ continues. $..$ Final Exam

$($b$)[20$ points$]$ Write the dynamic programming recurrences for both arrays, T and F