Which of the following statements are true for wave motion?

1. Mechanical transverse waves can propagate through all mediums

2. Longitudinal waves can propagate through solids only

3. Mechanical transverse waves can propagate through solids only

4. Longitudinal waves can propagate through a vacuum

(3) Hint: The mechanical transverse waves require shearing stress to travel.
When a mechanical transverse wave propagates through a medium, the constituent of the medium oscillates perpendicular to the wave motion causing a change in shape. That is each element of the medium is subjected to shearing stress. Solids and strings have shear modulus, which is why it results in shearing stress.
Fluids have no shape of their own, they yield to shearing stress. This is why transverse waves are possible in solids and strings but not in fluids.