How can I know if my brushes contain pig or hog hair? And for what purpose are these brushes actually used; acrylic, oil or watercolor?
Hog hair or hog bristle brushes are stiff, strong, and durable. Having frayed ends, the bristles are usually not appropriate for watercolouring, as they aren't able to soak up a lot of water, but they are sometimes used for adding texture or scrubbing away faulty layers of watercolour.
Exactly because they don't absorb a lot of fluid, they can be used well with oil and acrylic paints, as you can more easily move paint around. With their rough ('flagged') ends they don't allow for much precision, hence they are often formed into larger and rougher brushes, and can be used for covering larger areas, for grounding, or for more expressive approaches and impasto techniques.
However, by whipping the brush the ends will fray more, making the hairs softer, allowing them to be used for softer brushwork or even blending. This softening naturally occurs the longer you work with hog hair brushes.
To identify these brushes - which is not easy - you can look at the colour, and the structure of the hairs.
As organic hairs, they are usually quite easy to tell apart from synthetic ones (unless the latter are made to imitate animal hair), as the shafts are a lot more 'noisy' (see images below), both structure- and colour-wise.
Synthetic brushes also tend to have tops with much straighter cuts:
Another, surefire way to distinguish organic hairs from synthetic ones is to burn them: organic hairs will burn as separate threads, and have a distinctive bad smell, while synthetic hairs will melt together and smell of chemicals.
Hog/boar bristle brushes are (almost) always a broken white, and don't have a strong sheen to them, especially when compared to most synthetic hairs.
Sometimes a streak of black paint is added to make them look like badger hairs:
As mentioned before, hog hairs tend to fray at the tip, and this is visible in the brushes as having a distinctly diffuse tip, more so than with ox hair, for example:
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The hairs are also quite inexpensive, so the brushes are usually on the cheaper side of a producer's brush spectrum.
There aren't any clear-cut differences with other organic brushes, so I hope this is sufficient information to help you distinguish hog hair brushes from others.