$7.$ Now write code for each of the expressions below. Remember that they are written in standard mathematical notation, i$.$e$.$ multiplication and division precede addition and subtraction.

Note that you will have to convert the expressions to postfix $($reverse Polish$)$ notation first.

Do not reorder the calculations. If the problem asks for A $+$ B$,$ do not use the commutative law to replace that with B $+$ A$.$ Remember that A $+$ B $+$ C means $($A $+$ B$)+$ C$,$ not A $+($B $+$ C$).$ There are two reasons you should evaluate the expressions as written. First, you are trying to emulate the compiler. Second, although these pairs of expressions are equal for the small integers we are practicing with, that is not necessarily true for complex floating point calculations.

a$)$ X $=$ A $-$ B$*$C

b$)$ Y $=($A $-$ B$)*$C

c$)$ Do a$)$ and b$)$ calculate the same value, i$.$e$.,$ does X $=$ Y$?$ Why or why not?

d$)$ X $=($A $-$ B$)*($C $+$ D$)$

e$)$ X $=$ A $-($B$*$C $+$ D$)$

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