(A) : Mechanical transverse waves can propagate only in medium with shear modulus of elasticity
(B) : Longitudinal waves need bulk modulus of elasticity and are therefore. Possible in all media, solids, liquids and gases

The medium must possess the attribute of stiffness for transverse waves to propagate through it. Transverse waves cannot be formed in gases because they lack rigidity (they lack shear elasticity). On the other hand, solids may transmit both longitudinal and transverse waves because they have both volume and shear elasticity.