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