Question

To which rational number to which rational subset(s) does the following number belong?

Answer 1

Answer:

15 belongs to the set of natural numbers , whole numbers , integers & rational numbers.

Step-by-step explanation:

TO FIND :-

• those subsets to which 15 belongs

FACTS TO KNOW BEFORE SOLVING :-

N = Set of all natural numbers

W = Set of all whole numbers

Z = Set of all integers

Q = Set of all rational numbers

It can be said that :-

• N ⊂ W (∵ Whole numbers include all natural numbers along with 0)
• W ⊂ Z (∵ Integers include positive numbers i.e. whole numbers along with negative numbers.)
• Z ⊂ Q (∵ Rational numbers include all integers along with fractions.)

Hence , N ⊂ W ⊂ Z ⊂ Q

SOLUTION :-

Method 1 -

{15} ⊂ N (∵ 15 is an element of set N. {15} a singleton set & it can be called as the subset of N )

⇒ {15} ⊂ N ⊂ W ⊂ Z ⊂ Q

∴ 15 belongs to the set of natural numbers , whole numbers , integers & rational numbers too.

Method 2 -

• A rational number is a number which can be expressed in "p/q" form where p,q are integers & q ≠ 0. 15 can also be expressed as $\frac{15}{1}$. Hence, 15 is a rational number i.e. it belongs to the set of rational numbers.
• Natural numbers are the countable numbers. 15 is a countable number. So , 15 is a natural number i.e. 15 belongs to the set of natural numbers
• Whole numbers include all natural numbers as well as zero. 15 is a natural number. So , 15 is also a whole number i.e. 15 belongs to the set of whole numbers.
• Integers include the negative numbers as well as whole numbers. 15 is a whole number. So , 15 is also an integer i.e. 15 belongs to the set of all integers.