Lets verify the calculation of the maxterm $\backslash ($ M$\_5\backslash )$ for the $4$ Boolean variables $\backslash ($ A$,$ B$,$ C$,$ D $\backslash )$ and ensure that we correctly represent it in algebraic notation.### Steps to Determine the Maxterm $\backslash ($ M$\_5\backslash )1.**$Understanding Maxterms$**$: $-$ A maxterm is a product $($AND$)$ term that corresponds to a combination of variables that results in the output being $**0**.-$ Each maxterm is represented by the variables in their natural or complemented forms depending on whether the variable value is $1$ or $0,$ respectively$\mathrm{.}2.**$Binary Representation of $\backslash ($ M$\_5\backslash )**$: $-$ For $4$ variables $\backslash ($ A$,$ B$,$ C$,$ D $\backslash ),$ the decimal number $\backslash (5\backslash )$ in binary $($using $4$ bits$)$ is: $-$ Decimal $\backslash (5\backslash )=$ Binary $\backslash (0101\backslash )-$ This means: $-\backslash ($ A $=0\backslash )-\backslash ($ B $=1\backslash )-\backslash ($ C $=0\backslash )-\backslash ($ D $=1\backslash )3.**$Constructing the Maxterm$**$: $-$ Based on the binary representation: $-$ If a variable is $0$ in the binary representation, we take its negation. $-$ If a variable is $1$ in the binary representation, we take the variable itself. $-$ From $\backslash (0101\backslash )$: $-\backslash ($ A $=0\backslash )\backslash ($ A$\text{'}\backslash )($negated$)-\backslash ($ B $=1\backslash )\backslash ($ B $\backslash )-\backslash ($ C $=0\backslash )\backslash ($ C$\text{'}\backslash )($negated$)-\backslash ($ D $=1\backslash )\backslash ($ D $\backslash )4.**$Formulating $\backslash ($ M$\_5\backslash )**$: $-$ The maxterm for $\backslash ($ M$\_5\backslash )$ will be the $**$OR$**$ of the negated and non$-$negated variables: $\backslash [$ M$\_5=$ A$\text{'}+$ B $+$ C$\text{'}+$ D $\backslash ]$### ConclusionSo the algebraic representation for maxterm $\backslash ($ M$\_5\backslash )$ is:$\backslash [$M$\_5=$ A$\text{'}+$ B $+$ C$\text{'}+$ D$\backslash ]$This representation is indeed correct. If you have specific criteria or conditions you want to consider, please let me know!