Comparison by decimal representation:

• Lower bound: $\frac{3}{4} = 0.75$.
• Upper bound: $\frac{5}{6} \approx 0.833$.
• Evaluating the given fraction options:
  Option 1: $\frac{4}{5} = 0.80$, which satisfies $0.75 \lt 0.80 \lt 0.833$.
  Option 2: $\frac{3}{5} = 0.60$ ($\lt 0.75$).
  Option 3: $\frac{7}{5} = 1.40$ ($\gt 0.833$).
  Option 4: $\frac{6}{5} = 1.20$ ($\gt 0.833$).

Prime versus composite analysis among the given options:

• 31 is a prime number.
• 71 is a prime number.
• 101 is a prime number.
• 91 is a composite number because it is divisible by 7 and 13 ($91 = 7 \times 13$).
  Among the given options (31, 71, 91, 101), 91 is composite while all the others are prime numbers.

Mathematical verification of number system statements:

• Statement (A) is true: The set of non-negative integers $\{0, 1, 2, 3, \dots\}$ defines the whole numbers.
• Statement (B) is false: Integers include negative whole numbers ($\{\dots, -3, -2, -1\}$), zero, and positive numbers.
• Statement (C) is false: 91 is a composite number ($7 \times 13 = 91$).
• Statement (D) is true: Any integer $n$ can be expressed as a ratio of integers $\frac{n}{1}$ (where denominator $\ne 0$), making all natural numbers, whole numbers, and integers rational numbers.

Verification of mathematical definitions:

• Statement (A) is false: A prime number is a natural number strictly greater than 1 with exactly two distinct positive divisors (1 and itself). 0 is neither prime nor composite.
• Statement (B) is true: 1 is an integer ($\mathbb{Z}$).
• Statement (C) is false: 31 is a whole number and IS a prime number, having no divisors other than 1 and 31.
• Statement (D) is true: -31 is a negative integer ($\mathbb{Z}$), but whole numbers ($\mathbb{W}$) comprise only non-negative integers $\{0, 1, 2, \dots\}$.
  Statements (A) and (C) are not true (Option 1).