Number Set Membership Analysis

The question asks for a non-zero number that exists in all the following sets: Whole Numbers, Integers, Rational Numbers, and Real Numbers.

Let's define the sets and check the options:

• Whole Numbers (W): {0, 1, 2, 3, ...} (Non-negative integers)
• Integers (Z): {..., -2, -1, 0, 1, 2, ...} (Positive, negative, and zero whole numbers)
• Rational Numbers (Q): Numbers expressible as $p/q$, where $p, q$ are integers and $q \neq 0$. Includes integers, terminating, and repeating decimals.
• Real Numbers (R): All rational and irrational numbers.

Evaluating Options Based on Set Membership

The number must be non-zero.

• Option 1: 1
  • Is it non-zero? Yes.
  • Whole Number? Yes.
  • Integer? Yes.
  • Rational Number? Yes ($1/1$).
  • Real Number? Yes.
  • Conclusion: 1 belongs to all sets and is non-zero.
• Option 2: 0
  • Is it non-zero? No.
  • Conclusion: 0 is excluded because the question requires a non-zero number.
• Option 3: -1
  • Is it non-zero? Yes.
  • Whole Number? No. (Whole numbers are non-negative).
  • Integer? Yes.
  • Rational Number? Yes ($-1/1$).
  • Real Number? Yes.
  • Conclusion: -1 is excluded because it is not a Whole number.
• Option 4: $\sqrt{2}$
  • Is it non-zero? Yes.
  • Whole Number? No.
  • Integer? No.
  • Rational Number? No (it's irrational).
  • Real Number? Yes.
  • Conclusion: $\sqrt{2}$ is excluded because it is not Whole, Integer, or Rational.

Therefore, the only non-zero number that belongs to all four specified sets is 1.