Question

which of the following is set of number is not rational number ? a.natural b. whole c.real d.integer​

Answer 1

Answer- The above question is from the chapter 'Sets'.

Sets: Collection of well-defined objects is called a set.

Natural numbers: Counting numbers i.e. 1, 2, 3, 4, ... are called natural numbers.

Set of natural numbers is denoted by N.

Whole numbers: 0 and all natural numbers are called whole numbers.

Set of whole numbers is denoted by W.

Integers: Negatives of natural numbers, 0 and all positive natural numbers are called integers.

Set of integers is denoted by Z.

Rational numbers: Numbers which can be written in the form of p/q where p, q are integers and q ≠ 0 are called rational numbers.

Set of rational numbers is denoted by Q.

Real Numbers: Collection of rational and irrational numbers is called real numbers.

Set of real numbers is denoted by R.

Now, the order can be written like this:

Real numbers > Rational Numbers > Integers > Whole Numbers > Natural Numbers

Question: Which of the following is set of numbers is not rational numbers?

a. Natural

b. Whole

c. Real

d. Integer​

Solution: c. Real

Answer 2

ANSWER

option (c) real numbers

is your answer

EXPLANATION

ratinal numbers :-

• these are the numbers which can be written in the form of p/q form where p and q are integers and q not equal to 0
• note that 0/0 and any number/0 are not ratinal
• set of ratinal numbers is finite
• see chart

real numbers :-

• the set of real number contain ratinal and irrational numbers
• irrational number ( ex 2.22222 up to infinite ) can not be written in the form of p/q

CHART OF NUMBERS

there are two type of number

real number and non real number

• ratinal and irrational are subset of real numbers
• integers are subset of ratinal numbers
• whole numbers are subset of integers
• natural numbers are subset of natural numbers
• natural numbers start from 1 but whole numbers start from 0

SOME EXAMPLES

• Real = 2,3√5,√2
• irratinal = √5
• ratinal = 2/3
• Note :- since √2 is real but not ratinal
• whole num :- 0,1,2.....
• natural num :- 1,2,.....

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