**Core Concept**
The Enterobacteriaceae family is a group of Gram-negative bacteria that exhibit similar morphological and biochemical characteristics. This family includes various pathogens such as Salmonella, Shigella, and Escherichia. The key biochemical features of Enterobacteriaceae include the ability to ferment glucose, produce indole from tryptophan, and reduce nitrates.

**Why the Correct Answer is Right**
The correct answer states that all members of the Enterobacteriaceae family are oxidase positive. Oxidase is an enzyme that catalyzes the oxidation of reduced cytochrome c. In Enterobacteriaceae, the oxidase enzyme is associated with the periplasmic space and is encoded by the cyo operon. The presence of oxidase activity is a defining characteristic of this family, distinguishing them from other Gram-negative bacteria such as Pseudomonas and Vibrio, which are oxidase positive. The correct answer is a result of the biochemical and genetic features that are common to all members of the Enterobacteriaceae family.

**Why Each Wrong Option is Incorrect**
**Option A:** Motility in Enterobacteriaceae is typically achieved through a single polar flagellum, but it can also be mediated by peritrichous flagella or no flagella at all, depending on the species. Thus, stating that motility is exclusively by polar flagellum is incorrect.
**Option B:** Glucose is indeed fermented by all members of the Enterobacteriaceae family, which is one of the key biochemical characteristics of this group. Therefore, stating that glucose is not fermented by all members is incorrect.
**Option D:** Nitrate reduction is a common feature among many members of the Enterobacteriaceae family, particularly in the genera Escherichia, Salmonella, and Shigella. However, some species within this family may exhibit varying levels of nitrate reduction or even be unable to reduce nitrates. Nonetheless, stating that nitrate reduction is negative in all members is an overstatement.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that the biochemical characteristics of the Enterobacteriaceae family can vary between species. For instance, the ability to ferment lactose is a key differentiating feature between E. coli and Klebsiella pneumoniae. Understanding these biochemical features is crucial for accurate identification and diagnosis of infections caused by these bacteria.

**✓ Correct Answer: C. All members are oxidase positive**