Issues with Mysql installation on ubuntu

[kam saberi]

Hello,

I have troubles understanding and installing mysql 5.7 on ubuntu 20.04.

Before install I run the command and see the following:

$ dpkg --get-selections | grep mysql
libmysqlclient21:amd64 install
mysql-apt-config install
mysql-common install
mysql-community-client install
mysql-community-server deinstall
mysql-server-8.0 deinstall
mysql-workbench-community install
but when I run mysql from command line, I get the following message:

ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)
It appears to me that mysql server is not completely installed so I run the following command to do the install fresh but the error below:

I did some research but no matter what I do , this is not getting resolved.

Any help is greatly appreciated