\documentclass[14pt,a4paper,twocolumn,landscape]{arabart}
I propose the following code that generate the document showed in the picture above:
\documentclass[14pt,a4paper,twocolumn,landscape]{arabart}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%% importants packages %%%%%%%%%%%%%%%%%%%%%%
\usepackage[top=0.5cm, bottom=1.5cm, left=1cm, right=1cm]{geometry}
\usepackage[utf8]{inputenc}
\usepackage[LAE]{fontenc}
\usepackage[arabic]{babel}
\usepackage{multicol}
\usepackage{multirow}
\usepackage{tabularx}
\usepackage{amssymb}
\usepackage{array}
\usepackage{graphicx}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%% new command %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\dis}{\displaystyle}
\mathchardef\times="2202
\newcommand{\C}{\mathbb{C}}
\renewcommand{\R}{\mathbb{R}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\N}{\mathbb{N}}
\newcolumntype{Y}{>{\centering\arraybackslash}X}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%% page style %%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{fancyhdr}
\pagestyle{fancy}
\setlength{\columnseprule}{0.25pt}
\renewcommand{\footrulewidth}{1pt}%%%%footer%%%%%%%
\fancyfoot[C]{\textbf{ $\thepage$}} %%%%footer%%%%%
\fancyfoot[R]{
الاستاذ ................
} %%%%footer%%%%%%%
\fancyfoot[L]{ أكتوبر $2019$} %%%%footer%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\Large
%%%%%%%%%%%%%%%%%%%%%header%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\twocolumn[
\begin{@twocolumnfalse}
\begin{center}
\begin{tabularx}{\linewidth}{@{}YYY @{}}
\hline
& & \\
\AR{\textpetra{$1$ ب ع تجريبية -مادة الرياضيات-}} &
\AR{\textpetra{ تمارين مبادئ في المنطق }} &
\AR{\textpetra{ثانوية .......... التأهيلية}} \\
& & \\
\hline
\end{tabularx}
\end{center}
\hrulefill
\end{@twocolumnfalse}
]
%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%% EXERCICES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%exercice 1%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fbox{
التمرين
$1$:}\\
\AR{هل العبارات التالية صحيحة أم خاطئة؟ علل جوابك.
}
\\
$1$)
$(\forall x\in \mathbb{N})(\exists y \in \mathbb{N})(y=2x)$.
\\
$2$)
$(\forall x\in \mathbb{Q})(\exists y \in \mathbb{N})(y=2x)$.
\\
$3$)
$(\exists x \in \mathbb{N})(x^2=9)$.
\\
$4$)
$(\forall x \in \mathbb{Z})(\exists y \in \mathbb{Z})(x+y=7)$.
\\
$5$)
$(\forall x \in \mathbb{N})(x>0)$.
\\
$6$)
$(\exists x \in \mathbb{Q})(\forall y \in \mathbb{Q})(x+y=7)$.
\\
$7$)
$(\forall x \in \mathbb{Q})(\exists y \in \mathbb{Q})(xy=1)$.
\\
$8$)
$(\forall x\in \mathbb{Q})(\exists y \in \mathbb{Q})(y=\sqrt{x})$.
\\
$9$)
$(\exists x \in \mathbb{Q})(x^2=2)$.
\\
$10$)
$(\forall x\in \mathbb{R})(\forall y \in \mathbb{R})(x^2=y^2 \Longrightarrow x=y )$.
\hrule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% exercice 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fbox{
التمرين
$2$:}\\
بين أن:
\begin{center}
( $n$
فردي
)
$\Longrightarrow $( $ n^2$
فردي
)
$(\forall n \in \N);$
\end{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%
\hrule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% exercice 3 %%%%%%%%%%%%%
\fbox{
التمرين
$3$:}\\
\AR{
نعتبر العبارة
$\mathcal{P}$
:
$$\Big[ p\Longrightarrow \overline{\big(p\Longrightarrow q\big)} \Big]$$\hspace{2cm} }
حيث
$p$
و
$q$
عبارتين.
\vspace{0.3cm}\\
$1$)
اكتب
$\mathcal{P}$
باستعمال الروابط المنطقية: و , أو ,
$\neg$(النفي) .
\\
$2$)
بين التكافئ:
$\mathcal{P} \Longleftrightarrow \Big( p\Rightarrow \overline{q} \Big)$ . \\
\newpage
%%%%%%%%%%%%%%%% exercice 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fbox{
التمرين
$4$:}\\
حل النظمة التالية:
$$
\left\{
\begin{array}{ll}
2|x-1|-y=4 \\
|x|+2y=6 \\
\end{array}
\right.
$$
\hrule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% exercice 5 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fbox{
التمرين
$5$:}\\
\begin{center}
بين أن العدد
$n(n+1)(n+2)$
مضاعف للعدد
$3$
لكل
$n$
من
$\N$
\end{center}
\hrule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%% exercice 6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fbox{
التمرين
$6$:}\\
ليكن
$a$
عددا حقيقيا, بين أن:
$$(\forall \varepsilon >0); |a|<\varepsilon)\Longrightarrow a=0$$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\hrule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% exercice 7 %%%%%%%%%%%%%%%%%%%%%%%%%%%
\fbox{
التمرين
$7$:}\\
ليكن
$a$
و
$b$
عددين حقيقيين من المجال
$]-1,1[$,
بين أن:
$$-1<\dis\frac{a+b}{1+ab}<1$$
\hrule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%% exercice 8 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fbox{
التمرين
$8$:}\\
نعتبر الدالة العددية
$f$
المعرفة على
$\R$
بما يلي:
$$f(x)=2x^2-x+3$$
بين أن
$f$
ليست زوجية و لافردية.
\hrule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% exercice 9 %%%%%%%%%%%%%%%%
\fbox{
التمرين
$9$:}\\
بين أن:
$$(\forall x\in \R ^+); \dis\frac{1}{1+\sqrt{x}}=1-\sqrt{x} \Longrightarrow x=0 $$
\hrule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%% exercice 10 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fbox{
التمرين
$10$:}\\
ليكن
$a$
و
$b$
عددين حقيقيين بحيث
$a^2+b^2=1$
, بين أن:
$$|a+b|\leqslant \sqrt{2}$$
\hrule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% exercice 11 %%%%%%%%%%%%%%%%%%%
\fbox{
التمرين
$11$:}\\
\\
بين أن
$\sqrt{6}\notin \Q$
و
$\sqrt{2}+\sqrt{3}\notin \Q$
\\
\hrule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% exercice 12 %%%%%%%%%%%%%%%%%%%%%
\fbox{
التمرين
$12$:}\\
\\
بين أن
$11$
يقسم
$3^{2n}+2^{6n-5}$
لكل
$n$
من
$\N^*$
\vspace{0.25cm}
\hrule
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%% exercice 13 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fbox{
التمرين
$13$:}\\
بين أن:
\begin{flushright}
$
\forall (x,y)\in \R^2$
$$ \big(x+\sqrt{x^2+1} \big) \big(y+\sqrt{y^2+1} \big)=1 \Leftrightarrow x+y=0 $$
\end{flushright}
\end{document}
I hope this was useful.
