Assertion: Solids can support both longitudinal and transverse waves but only longitudinal waves can propagate in gases.
Reason: For the propagation of the transverse waves, the medium must also necessarily have the property of rigidity.
A. Both Assertion and Reason are correct and reason is a correct explanation for Assertion.
B. Both Assertion and Reason are correct and reason should not be an explanation for Assertion.
C. Assertion is correct but reason is incorrect.
D. Both assertion and reason are.

Hint:In order to answer this question, to know whether the given reason is correct of the given assertion, and then we will also explain the reason behind the assertion and the given reason and then we will talk much more about the types of waves.

Complete answer:
The medium must be stiff in order for transverse waves to propagate. Transverse waves cannot be formed in gases because they lack rigidity (they lack shear elasticity). Solids, on the other hand, have both volume and shear elasticity, and can transmit both longitudinal and transverse waves.

Or in other words, the stiffness of the medium is required for the propagation of transverse waves. Because gases lack stiffness (and so lack shear elasticity), transverse waves cannot be generated in them. Solids, on the other hand, have both volume and shear elasticity, as well as the ability to transmit both longitudinal and transverse waves.

Transverse waves produce shear, but because gases lack shear modulus and are unable to sustain shear, they can only propagate longitudinal waves. Solids can propagate both transverse and longitudinal waves and have both shear and bulk modulus of elasticity.

Transverse wave motion occurs when all points on a wave oscillate along pathways that are perpendicular to the wave's advance direction. Transverse waves include water surface ripples, seismic S (secondary) waves, and electromagnetic (e.g, radio and light) waves.Therefore, both assertion and reason are correct and reason is a correct explanation for assertion.

Hence, the correct option is A.

Note: Transverse waves are most commonly generated in elastic substances when solid particles are moved from their starting position and oscillate in directions perpendicular to the wave's propagation. By rapidly moving a rope up and down, a rudimentary demonstration of this wave can be made.