Section in greek is not bold

Question

I am trying to write the solution to some exercises in greek, but I cannot get the section to be bold and underlined if I use greek letters. It might be worth noting that:

1. It works fine if I use \textlatin{Ex 1}
2. Using \section*{\pmb{\underline{Άσκηση 1}}} gives me exactly what I am looking for

Here is my code with all the packages I am using:

% Set the font (output) encoding
\usepackage[LGR]{fontenc}
% Greek-specific commands
\usepackage[greek]{babel}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage[utf8]{inputenc} % Required for inputting international characters
\usepackage{alphabeta}
\usepackage[T1]{fontenc} % Output font encoding for international characters
\usepackage{mathpazo} % Palatino font
\usepackage{tgtermes}
\usepackage{amsmath}
\usepackage{indentfirst}
\usepackage{geometry}
\usepackage[margin=0.5in]{geometry}
\usepackage{amsthm}
\newtheorem{theorem}{Θεώρημα}[section]
\newtheorem{lemma}[theorem]{Λήμμα}
\usepackage{etoolbox}
\usepackage[tableaux]{prooftrees}
\renewcommand*\linenumberstyle[1]{(#1)}
\usepackage{hyperref}

\begin{document}
\section*{Άσκηση 1}}
Καλημέρα
\end{document}

Answer 1

I have followed the suggestion of the user @miltos: I have put \usepackage[T1,LGR]{fontenc} and I shoudn't load inputenc at all. The problem it is the sovrapposition of mathpazo and tgtermes font packages that cause the problem.

\documentclass[a4paper,12pt]{book}
\usepackage[LGR,T1]{fontenc}
% Greek-specific commands
\usepackage[greek]{babel}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{alphabeta}
\usepackage{indentfirst}
\usepackage[margin=0.5in]{geometry}
\usepackage{amsthm}
\newtheorem{theorem}{Θεώρημα}[section]
\newtheorem{lemma}[theorem]{Λήμμα}
\usepackage{etoolbox}
\usepackage[tableaux]{prooftrees}
\renewcommand*\linenumberstyle[1]{(#1)}
\usepackage{hyperref}

\begin{document}
\section*{Άσκηση 1}
Καλημέρα \textbf{Καλημέρα}
\end{document}

Answer 2

You need to use a font family that supports the Greek alphabet, but mathpazo doesn't, nor does tgtermes.

By the way, it's rather strange to use Times (which tgtermes provides a clone of) for text and Palatino (provided by mathpazo) for math.

If you don't know what a package does, don't load it.

If you look in the log file, you find

LaTeX Font Warning: Font shape `LGR/qtm/m/n' undefined
(Font)              using `LGR/cmr/m/n' instead on input line 18.

LaTeX Font Warning: Font shape `LGR/qtm/b/n' undefined
(Font)              using `LGR/qtm/m/n' instead on input line 25.

The first warning is the most important: it tells you that the font family qtm (from tgtermes) doesn't support the LGR (Greek) encoding, so it substitutes it with a default, in this case the Beccari fonts that are known to LaTeX as cmr for LGR.

The next warning is similar: when LaTeX wants to set the section title, it tries boldface, but realizes that there is no bold LGR font in the qtm family, so it substitutes it with the alias it had created on the fly at the time of the first warning. No boldface.

If your document uses math, you need to choose a font family that supports both Greek and math. If you want (a clone of) Times, you can use Tempora for text and NewTX for math.

I had to change the order of package loading, because amsmath and amssymb (loaded by prooftrees) have to be before newtxmath.

I left geometry, but the setting of a 0.5in margin is rather bizarre.

\documentclass[a4paper]{article}
\usepackage[margin=0.5in]{geometry}
%\usepackage[LGR]{fontenc}
\usepackage[greek]{babel}

\usepackage{amsmath}
\usepackage{amsthm}
\usepackage[tableaux]{prooftrees}
\usepackage{tempora,newtxmath}

\usepackage{graphicx}
\usepackage{indentfirst}
\usepackage{etoolbox}
\usepackage{hyperref}

\newtheorem{theorem}{Θεώρημα}[section]
\newtheorem{lemma}[theorem]{Λήμμα}
\renewcommand*\linenumberstyle[1]{(#1)}

\begin{document}

\section*{Άσκηση 1}

Καλημέρα $a+b=c$

\end{document}