This question has multiple correct options
(A) In polar aprotic solvents such as DMSO, DMF, and DMA, the fugacity order is c
(B) strong bases are good leaving groups.
(C) The leaving group order of the following is: $O{{H}^{-}}>R{{O}^{-}}>CH$=\[{{C}^{-}}>N{{H}_{2}}^{-}\]
(D) Charged species are better leavings than neutral species.

Hint: Solvents are generally classified by the polarity and considered either polar or nonpolar as indicated by the dielectric constant. The protic and aprotic solvents, distinguishing the feature of an –OH group, and that is the most common characteristic of an aprotic solvent. The nature of the leaving groups depends on whether the species are strong base or weak base.

Complete answer:
(A) The leaving group should be able to stabilize the additional electron density that results from the bond in polar aprotic solvents.
DMSO=dimethyl sulfoxide is very polar
DMF = dimethyl formamide is a polar aprotic solvent
DMA=dimethyl acetamide is also a polar aprotic solvent
The polar aprotic solvents favor SN1 reactions.
The fugacity order in given polar aprotic solvents is ${{I}^{-}}>B{{r}^{-}}>C{{l}^{-}}>{{F}^{-}}$ because the size of the ion increases basicity increase, hence nucleophilicity decreases. So nucleophilicity is directly proportional to fugacity.
As the electronegativity increases, the ability of the leaving group increases, and also the weaker base stronger is leaving groups.
Stronger bases are not good leaving groups, because leaving groups are able to accept electrons, but strong bases are not able to donate electrons due to their decrease in electronegativity.

Basic order: \[O{{H}^{-}} < R{{O}^{-}} < CH\equiv {{C}^{-}} < N{{H}_{2}}^{-}\]

The leaving group order:
                    \[O{{H}^{-}}>R{{O}^{-}}>CH\equiv {{C}^{-}}>N{{H}_{2}}^{-}\]

In organic reactions, a conjugate base that is weakly bases is stronger leaving groups than neutral species. For example, $HS{{O}_{4}}^{-}>N{{H}_{3}}$
So, the correct answer is “OptionA, C and D”.

Note: Some factors will determine if a species wants to share its electrons, or not include electronegativity, size, and resonance. Weak bases are strong leaving groups, then EN values increase, size increases, and more resonance will decrease the basicity. Then obviously the ability to leave the group will increase.