Final answer:
Option (c), Rosacea is the condition known for presenting as redness and swelling of the face with flushing. Erysipelas also involves intense facial inflammation, but with clear borders, and is usually caused by an infection.
Step-by-step explanation:
The condition that presents as redness and swelling of the face with flushing is rosacea. Rosacea is a chronic skin condition characterized by facial redness, swelling, and, often, acne-like breakouts. While conditions like acne vulgaris, erysipelas, and systemic lupus erythematosus (SLE) can cause facial redness, they are associated with other distinct symptoms.
Erysipelas, caused by Streptococcus pyogenes, presents as a large, intensely inflamed patch of skin, often on the legs or face, but with well-demarcated borders. On the other hand, acne is a result of clogged, sebum-filled pores that become inflamed, often leading to pus-filled lesions. Lastly, SLE might cause facial redness in the form of a butterfly rash but is generally associated with a wide range of systemic symptoms beyond just facial flushing.