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All real numbers are rational numbers. A) True B) False

All real numbers are rational numbers.
A) True
B) False

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60782 Points
one year ago
Hint: We will first define the real number and rational number. Real numbers are numbers which are formed from the combination of both rational numbers and irrational numbers and rational number is defined as a number which can be expressed in the form of pq, where p and q are integers and q cannot be zero. We will use these definitions to check the given statement. Complete step by step solution: Here we need to check whether all real numbers are rational numbers or not. We know that the real numbers are numbers which are formed from the combination of both rational numbers and irrational numbers and rational number is defined as a number which can be expressed in the form of pq , where p and q are integers and q cannot be zero Thus, we can say that numbers which are not rational numbers are called irrational numbers. If we combine the rational numbers and the irrational numbers, we get real numbers. Hence, all real numbers are not rational numbers because real numbers also contain irrational numbers. Hence, the given statement is false. Therefore, the correct option is option B. Note: Rational and irrational are opposite to each other. Rational numbers can be expressed as the ratio of two integers - hence the name rational. An Irrational is any number which is not rational. So every rational number is certainly not irrational. Rational numbers and irrational numbers are mutually exclusive. Therefore, every rational number is sure not to be a irrational number and every irrational number is sure not to be a rational number.

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