Here's an argument with a true premise:
- The capital of France is Paris.
- General Patton died in Nottingham.
- If General Patton died in Nottingham, then he died where Robin Hood lived.
- Therefore, Robin Hood lived in Nottingham.
Premise (1) is true. It is utterly irrelevant to the argument, but true. Also, the argument is invalid, since (4) doesn't follow from the preceding premises, and sound arguments must be valid.
However, even if a true premise were used relevantly in the argument, it wouldn't necessarily be sound:
- The Earth revolves around the Sun.
- Either the Earth doesn't revolve around the Sun, or Germany is in Asia.
- Therefore, Germany is in Asia.
This argument, while deductively valid, is unsound, even though premise (1) is true. That's because premise (2) is false.
To be deductively sound, every premise must be true and the argument must be deductively valid.