- Iron is always magnetic
- A magnet attracts magnetic metals
- Hence, a magnet will attract iron

- A magnet will attract iron
- The mixture is made of iron nails and aluminum nails
- Hence, a magnet will attract the iron nails in the mixture

- A magnet will not attract nonmagnetic metals
- Aluminum is always nonmagnetic
- Hence, a magnet will not attract aluminum

- A magnet will not attract aluminum
- The mixture is made of iron nails and aluminum nails
- Therefore, a magnet will not attract the aluminum nails in the mixture

- A magnet will attract the iron nails in the mixture
- A magnet will not attract the aluminum nails in the mixture
- Therefore, a magnet can separate the mixutre of iron nails and aluminum nails

Therefore, a magnet can separate the mixutre of iron nails and aluminum nails
A strong magnet will separate a mixture of
- A magnet will not attract nonmagnetic metals 
- Aluminum is always nonmagnetic 
- The mixture is made of iron nails and aluminum nails 
- Iron is always magnetic 
- A magnet attracts magnetic metals