Question

Which of the following statement is true? *

1 point

ਹਰੇਕ ਅਪਰਿਮੇਯ ਸੰਖਿਆ ਇੱਕ ਵਾਸਤਵਿਕ ਸੰਖਿਆ ਹੈ। (Every irrational number is a real number)

ਹਰੇਕ ਪਰਿਮੇਯ ਸੰਖਿਆ ਇੱਕ ਪੂਰਨ ਸੰਖਿਆ ਹੈ। (Every rational number is a whole number)

ਹਰੇਕ ਸੰਪੂਰਨ ਸੰਖਿਆ ਇੱਕ ਪੂਰਨ ਸੰਖਿਆ ਹੈ। (Every integer is a whole number)

ਹਰੇਕ ਵਾਸਤਵਿਕ ਸੰਖਿਆ ਇੱਕ ਅਪਰਿਮੇਯ ਸੰਖਿਆ ਹੈ। (Every real number is an irrational number)

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Answer 1

Answer:

every integer is a whole number

Answer 2

Answer:

Option(a) Every irrational number is a real number.

Step-by-step explanation:

Given:  Four statements - every irrational number is a real number, every rational number is a whole number,every integer is a whole number, every real number is an irrational number.

To find: Which statement is true.

Solution:

We will check each statements.

(1) Every irrational number is a real number.

Irrational numbers- These are numbers which cannot be written in the form p/q, where p and q are integers and q≠0. Eg; √3, √2, √5, π,etc.

Real numbers consist of both rational and irrational numbers.

So irrational numbers are subsets of real numbers and irrational numbers belongs to real numbers.

Therefore Option (1) is true, every irrational number is a real number.

(2) Every rational number is a whole number.

Rational number is a number which can be written in the form p/q, where p and q are integers, q≠0. Both the numerator and denominator should be integers.

Whole numbers- 0 and the natural numbers are called whole numbers.

0 (a whole number) cannot be in the denominator of rational numbers and whole numbers are not fractions.

Eg; 2/1= 2 is a rational number and also a whole number, but 1/3 is a rational number and not a whole number. So all rational numbers won't be a whole number but all whole numbers can be written as rational number.

Whole number is a subset of rational number.

Therefore,Option(2) false. Every rational number is not a whole number.

(3) Every integer is a whole number.

0 and the natural numbers are called whole numbers.

integer consist of negative numbers,zero and the positive numbers. So whole numbers are subset of integers. Eg; -1 ∉ whole numbers.whole numbers are integers but all integers are not a whole number.

Therefore, option(3) is false, every integer is not a whole number.

(4) Every real number is an irrational number.

irrational number are numbers which cannot be written in the form p/q, where p and q are integers,q≠0. √2, √5, π,etc.

real numbers consist of rational and irrationals. Irrational number is a subset of real numbers.

Therefore, option(4) is false, every real number is an irrational number.

Thus option (1) is true.

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