Customized true/false questions in exam document class

Question

In the upcoming exam I plan to have one exercise in the form of MC questions. I use the exam document class and usually use something like this:

\documentclass{exam}

\begin{document}
\begin{questions}
\question

Please answer the following questions by ticking the correct answers. Note that
multiple answers may be correct. One point can be earned per question.

Only completely correct solutions will be evaluated. In that case, you will
receive one point, otherwise zero.

\begin{parts}

\part Which of the following statements describes \dots?
\begin{checkboxes}
    \CorrectChoice This one
    \choice Or that one
    \CorrectChoice Perhaps this
    \choice Or that
\end{checkboxes}

\part Which of the following criteria are included in \dots?
\begin{checkboxes}
    \CorrectChoice This one
    \choice Or that one
    \CorrectChoice Perhaps this
    \choice Or that
\end{checkboxes}
\end{parts}
\end{questions}
\end{document}

So usually that just works fine and I have a handful of parts in this question section.

No I was wondering if it is possible to render the third part of the same question section as follows (the number "1." should actually be "3."):

Answer 1

See if this helps:

\documentclass{exam}
\usepackage{amssymb}
% \printanswers

\newcommand*{\TrueFalseChoice}[1]{%
\ifprintanswers
    \ifthenelse{\equal{#1}{T}}{%
        $\checkmark$
    }{
        $\square$
    }
\else
    $\square$
\fi
} 

\begin{document}
\begin{questions}
\question
\begin{parts}

\part True/False questions\\
\begin{tabular}{lcc}
    Statements & True & False \\
    First statement & \TrueFalseChoice{T} & \TrueFalseChoice{F} \\
    First statement & \TrueFalseChoice{F} & \TrueFalseChoice{T}
\end{tabular}

\end{parts}
\end{questions}

\end{document}