No. Electromagnetic waves travel through vacuum ( ie space where there is nothing)
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Seismic, or earthquake waves travel through the earth. They may travel through our crust, which is rocky, or through the more fluid parts, like the mantle, but the medium is the earth.
Electro-magnetic waves of many kinds travel through certain solids and liquids: radio waves (these are waves of relatively low frequency/high wavelength) can travel through almost anything. Microwaves - shorter wavelength, higher frequency - need particular materials to stop them. Gamma rays (a form of radioactivity) can pass through many solids, and need a very thick layer of a dense metal such as LEAD to stop them. Visible light, which is also a form of electro-magnetic radiation - can (obviously) travel through some liquids and solids; those which are to some extent transparent.Sound waves - which are pressure waves - can also travel through solids and liquids.Generally, the answer to the question varies according to which solids and liquids are being considered; and each of these will permit a different range of waves to pass through them.
We are talking about the seisimc waves in an earthquake. The difference in the speed of travel of the two waves has to do with what has to happen to the medium (the ground or the earth) to transmit the energy of the seismic wave. Let's look. The P wave is a longitudinal wave or a compression wave. The force is applied in the direction that the wave is traveling. The ground must move in that direction. Ground or earth is pretty incompressible, so the energy is transferred pretty quickly. In the S wave, the medium is displaced in a transverse (up and down - compared to the line of travel) way, and the medium must shear or "move away" from the material right next to it to cause the shear and transmit the wave. This takes more time, and this is why the S wave moves more slowly than the P wave in seismic events. Need a link to seismic waves? You got it. Wikipedia has a good article, and the pictures are worth the trip over to view them.
Radiation is when heat is transferred from one thing to another via electromagnetic waves like infrared. It can travel through a vacuum. Convection is when a fluid is heated from the bottom and rises, leaving colder fluid behind to be heated etc creating currents. The thing you are trying to heat has to be in contact with the heat source- it doesn't work through a vacuum.
because there is no medium, conduction and convection need medium to spread through, they cannot spread through vacuum.