I'd like to clarify that you can sort of get one without the other, at DC, or zero frequency.

If you have a steady flow of electricity, you get a steady magnetic field. But once the electricity oscillates in any way, you start emitting EM radiation.

Likewise, a magnet emits a steady magnetic field. Move the magnet and you induce an electric field.

Additionally, light is a transverse wave of orthogonally oriented oscillating electric and magnetic fields. Yikes....not exactly in layman's English, is that? Sorry. If anyone's interested, I can clarify further. Or is your brain too mushy already? :)

Brian