Q$1.$ For a given sentence: "Cat sat on the mat", construct a constituent tree using the following production rules: Written $[5]$

$\backslash [$

$\backslash$begin$\{$array$\}\{$l$\}$

$\backslash$mathrm$\{$S$\}\backslash$rightarrow $\backslash$mathrm$\{$VP$\}\backslash \backslash$

$\backslash$mathrm$\{$VP$\}\backslash$rightarrow $\backslash$text $\{$ NP V PP $\}\backslash \backslash$

$\backslash$mathrm$\{$NP$\}\backslash$rightarrow $\backslash$text $\{$ DET ADJ N $\}\backslash \backslash$

$\backslash$mathrm$\{$PP$\}\backslash$rightarrow $\backslash$text $\{$ P NP $\}\backslash \backslash$

$\backslash$mathrm$\{$NP$\}\backslash$rightarrow $\backslash$text $\{$ DET $\}\backslash$mathrm$\{$N$\}$

$\backslash$end$\{$array$\}$

$\backslash ]$

$-$ First, identify the main verb in the sentence and draw a horizontal line to represent the root node of the tree. This will be the starting point for the rest of the tree.

$-$ Identify the subject of the verb and draw a vertical line coming off the root node. Label this line with the word $"$NP$"$ for noun phrase.

$-$ Identify any direct objects or indirect objects of the verb and draw additional vertical lines coming off the root node. Label these lines with the word $"$NP$"$ as well.

$-$ For each noun phrase, determine what words make up the phrase. These can include determiners $($e$.$g$.$ "the," $"$a$,""$an$"),$ adjectives, and nouns. Draw horizontal lines coming off the noun phrase lines to represent each of these words and label them with the appropriate part of speech $($e$.$g$.$ "DET," "ADJ," $"$N$").$

$-$ If the sentence has any modifying phrases or clauses, draw additional lines coming off the relevant words in the tree and label them with the appropriate constituent label $($e$.$g$."$PP$"$ for prepositional phrase, "SBAR" for subordinating clause$).$

$-$ Continue this process until you have identified and labeled all of the constituents in the sentence.