📘 Question
Are the following statements true or false? Give reasons:
- (i) Every whole number is a natural number.
- (ii) Every integer is a rational number.
- (iii) Every rational number is an integer.
- (iv) Every natural number is a whole number.
- (v) Every integer is a whole number.
- (vi) Every rational number is a whole number.
✏️ Solutions
(i) Every whole number is a natural number → False
Reason: Whole numbers include 0, but natural numbers start from 1.
—(ii) Every integer is a rational number → True
Reason: Any integer \(n = \frac{n}{1}\), so it is rational.
—(iii) Every rational number is an integer → False
Reason: \(\frac{1}{2}\) is rational but not an integer.
—(iv) Every natural number is a whole number → True
Reason: Whole numbers include all natural numbers and 0.
—(v) Every integer is a whole number → False
Reason: Negative integers are not whole numbers.
—(vi) Every rational number is a whole number → False
Reason: Fractions like \(\frac{3}{2}\) are rational but not whole.
—✅ Final Answers Summary
- (i) False
- (ii) True
- (iii) False
- (iv) True
- (v) False
- (vi) False
💡 Key Concept
- Natural ⊂ Whole ⊂ Integer ⊂ Rational
- Each larger set contains the smaller ones