The following statements are given with respect to the symmetry operations and symmetry elements.
A. BF₃ possesses an S₃ axis
B. C₂H₆ in a staggered conformation possesses an S₆ axis
C. Benzene molecule possesses three σ_v - planes
D. Water molecule possesses C₂ axis and σ_h - plane
The option giving the correct statements, is

Correct option is B

The systematic discussion of symmetry is called group theory. An action that leaves an object looking the same after it has been carried out is called a symmetry operation. Typical symmetry operations include rotations, reflections, and inversions. There is a corresponding symmetry element for each symmetry operation, which is the point, line, or plane with respect to which the symmetry operation is performed.
The classification of objects according to symmetry elements corresponding to operations that leave at least one common point unchanged gives rise to the point groups.
The identity, E, consists of doing nothing; the corresponding symmetry element is the entire object.
An n-fold rotation (the operation) about an n-fold axis of symmetry, C_n (the corresponding element) is a rotation through 360°/n. If a molecule possesses several rotation axes, then the one (or more) with the greatest value of n is called the principal axis.
A reflection (the operation) in a mirror plane, σ (the element), may contain the principal axis of a molecule or be perpendicular to it. If the plane is parallel to the principal axis, it is called ‘vertical’ and denoted σ_v . A vertical mirror plane that bisects the angle between two C₂ axes is called a ‘dihedral plane’ and is denoted σ_d . When the plane of symmetry is perpendicular to the principal axis it is called ‘horizontal’ and denoted σ_h.
An n-fold improper rotation (the operation) about an n-fold axis of improper rotation or an n-fold improper rotation axis, S_n, (the symmetry element) is composed of two successive transformations. The first component is a rotation through 360°/ n, and the second is a reflection through a plane perpendicular to the axis of that rotation; neither operation alone needs to be a symmetry operation.
If in addition to the identity and a C_n axis a molecule has n vertical mirror planes σ_v , then it belongs to the group C_nv.
A molecule that has an n-fold principal axis and n two fold axes perpendicular to C_n belongs to the group D_n. A molecule belongs to D_nh if it also possesses a horizontal mirror plane.
A molecule belongs to the group D_nd if in addition to the elements of D_n it possesses n dihedral mirror planes σ_d. The staggered conformation of ethane belongs to D_3d.

Benzene  belongs to D_6h . The symmetry elements are:

Figure shows all the symmetry elements for the water molecule. By convention, the rotation axis of highest symmetry (principal rotation axis), C₂ , is oriented along the z axis. The C₂ axis passes through the O atom. The molecule has two mirror planes oriented at 90° to one another, and their line of intersection is the C₂ axis.

BF₃ belongs to D_3h .The symmetry elements are:

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