Consider the following statements :
1. The set of all irrational numbers between and is an infinite set.
2. The set of all odd integers less than 100 is a finite set.
Which of the statements given above is/are correct?

Question

Question

This question was previously asked in

NDA 02/2022 Mathematics Official Paper (Held On 04 Sep 2022)

Answer 1

Concept:

Between any two real numbers, there are infinitely many rationals and irrational.

{The numbers which are not rational are irrational}

Real = Rational ∪ Irrational

Explanation:

1. The set of all irrational numbers between and is an infinite set.

There are infinitely many rationals and irrational between any two real numbers.

and are two irrational numbers and there are infinitely many rationals and irrationals between them.

⇒ The set of all irrational numbers between and is an infinite set.

So, statement 1 is true.

2. The set of all odd integers less than 100 is a finite set.

The set of all odd integers less than 100 is given by

{......,-5 ,-3 ,-1 ,1 ,3 ,5 ,.....,95, 97, 99}

this set is bounded above but not bounded below

So, It is an infinite set, and statement 2 is false.

∴ The correct option is (1).

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