To solve this question, let's analyze each of the statements presented: I. All waves change wavelength when changing medium without changing frequency. - This statement is true. When a wave passes from one medium to another, its wavelength can change due to the change in the wave's propagation speed. However, the frequency of the wave remains constant, as it is a characteristic of the wave's source. II. All waves propagate in a vacuum. - This statement is false. Mechanical waves, such as sound waves, require a material medium to propagate and cannot propagate in a vacuum. On the other hand, electromagnetic waves, like light, can propagate in a vacuum. III. All waves carry energy without carrying matter. - This statement is true. Waves are disturbances that carry energy from one point to another without the transport of matter. This is valid for both mechanical waves and electromagnetic waves. IV. All waves experience the phenomena of reflection, refraction, diffraction, interference, and polarization. - This statement is partially true. All types of waves can experience reflection, refraction, diffraction, and interference. However, polarization is a specific phenomenon of transverse waves, such as electromagnetic waves. Longitudinal mechanical waves, like sound, do not exhibit polarization. Based on the analysis, statements I, III, and IV (with the note about polarization) are true, while statement II is false. Therefore, the correct answer is: c) i, iii, and iv.