The Following Is Dr

The following is Dr. Hernandez's differential diagnosis for her patient, who has a rash and has developed difficulty with her toenails. DDx:
1) Rash: Plaque psoriasis, seborrheic dermatitis, atopic dermatitis.
2) Onycholysis: Psoriatic vs. onychomycosis.
Which of the following is NOT true?

A) The patient is losing her nail.
B) The patient may have a fungal condition of the nail.
C) The rash may be an unusual inflammation of the skin.
D) The rash may be an unusual inflammation of the skin caused by the discharge of oil.
E) The rash may be caused by fungus.