Electromagnetic waves are transverse in nature. According to the electromagnetic theory:

1. The oscillating electric field ($\mathbf{E}$) and magnetic field ($\mathbf{B}$) are perpendicular to each other and both are perpendicular to the direction of propagation of the wave . Therefore, the statement that they are parallel to each other is false.
2. Both fields oscillate in phase, meaning they attain their maxima and minima at the same place and time.
3. Electromagnetic waves do not require any material medium for propagation and can travel through a vacuum .
4. The energy associated with the electromagnetic wave is shared equally between the electric and magnetic fields.