Among the following statements, the statement which is not correct is :

Options

A. a)Every rational number is a real number
B. b)Every real number is a rational number
C. c)Every integer is a rational number
D. d)Every natural number is an integer

Answer

To solve the question, we need to evaluate the given statements about the number system and identify which one is incorrect. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Number System
- The number system includes different categories of numbers: natural numbers, whole numbers, integers, rational numbers, and real numbers.
- Natural numbers are positive integers starting from 1 (1, 2, 3, ...).
- Whole numbers include natural numbers and zero (0, 1, 2, 3, ...).
- Integers include all whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3, ...).
- Rational numbers can be expressed as the fraction of two integers (P/Q where Q ≠ 0).
- Real numbers include both rational and irrational numbers.

### Step 2: Analyze Each Statement
1. **Statement A**: Every rational number is a real number.
- This statement is **true** because all rational numbers can be represented on the number line.

2. **Statement B**: Every real number is a rational number.
- This statement is **false**. Real numbers include both rational numbers (like 1/2, 3) and irrational numbers (like √2, π), which cannot be expressed as a fraction of two integers.

3. **Statement C**: Every integer is a rational number.
- This statement is **true** because any integer can be expressed as a fraction (e.g., -3 can be written as -3/1).

4. **Statement D**: Every natural number is an integer.
- This statement is **true** because natural numbers (1, 2, 3, ...) are part of the integer set.

### Step 3: Identify the Incorrect Statement
- From the analysis, we see that Statement B is the only incorrect statement.

### Conclusion
The statement which is not correct is **Statement B**: "Every real number is a rational number."

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