Final answer:
Most EU member countries have indeed adopted the euro as the common currency since its introduction in 1999, with notable exceptions such as the United Kingdom, Denmark, and Sweden.
Step-by-step explanation:
The statement that most member countries adopted the common currency, which in the European Union (EU) is the euro, is true.
The euro was introduced in 1999 and initially used for commercial and financial transactions in eleven EU countries. By the start of 2002, euro notes and coins became the legal currency in the majority of EU countries.
While the euro has been accepted by most EU members, it is important to note that some countries like the United Kingdom, Denmark, and Sweden decided to keep their own currencies.
In addition to EU members, there are countries not currently in the EU that have also adopted the euro as their national currency. However, the process of adopting the euro is not simple and often requires a country to meet specific economic criteria and to give up certain controls over their own monetary policy.