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Boyle's law relates volume to pressure. As volume decreases pressure increase. In the case of the example, squeezing the bottle reduces the volume. On a particle level, the number of particles remains the same, and since the temperature of the air doesn't change the speed of the particles remains constant. However, the volume in which the particles bounce around in decreases therefore the number of collisions between the particles and the inner surface of the water bottle increases. This is pressure.

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