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Consider the following statements :
1. The set of all irrational numbers between 2 and 5 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?
1. The set of all irrational numbers between 2 and 5 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?
- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 nor 2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Consider the following statements :1. The set of all irrational number...
Concept:
Between any two real numbers, there are infinitely many rationals and irrational.
{The numbers which are not rational are irrational}
Real = Rational ∪ Irrational
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 √2 and √5 is an infinite set.
There are infinitely many rationals and irrational between any two real numbers.
√2 and √5 are two irrational numbers and there are infinitely many rationals and irrationals between them.
⇒ The set of all irrational numbers between √2 and √5 is an infinite set.
So, statement 1 is true.
1. The set of all irrational numbers between √2 and √5 is an infinite set.
There are infinitely many rationals and irrational between any two real numbers.
√2 and √5 are two irrational numbers and there are infinitely many rationals and irrationals between them.
⇒ The set of all irrational numbers between √2 and √5 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).
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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Community Answer
Consider the following statements :1. The set of all irrational number...
Statement 1: The set of all irrational numbers between 2 and 5 is an infinite set.
An irrational number is a number that cannot be expressed as a fraction of two integers. It is a decimal that goes on forever without repeating.
To determine whether the set of all irrational numbers between 2 and 5 is infinite, we need to consider the nature of irrational numbers.
- There are infinitely many irrational numbers between any two rational numbers.
- The set of irrational numbers is not countable, meaning it cannot be listed in a finite or countable sequence.
Since the set of irrational numbers between 2 and 5 is a subset of the set of all irrational numbers, it follows that the set of irrational numbers between 2 and 5 is also infinite.
Therefore, statement 1 is correct.
Statement 2: The set of all odd integers less than 100 is a finite set.
To determine whether the set of all odd integers less than 100 is finite, we need to consider the definition of a finite set.
A finite set is a set that has a specific number of elements and can be counted or listed.
In this case, the set of all odd integers less than 100 includes numbers like 1, 3, 5, 7, 9, ... up to 99.
Since we can list or count all the elements in this set, it is a finite set.
Therefore, statement 2 is incorrect.
Conclusion:
- Statement 1 is correct as the set of all irrational numbers between 2 and 5 is infinite.
- Statement 2 is incorrect as the set of all odd integers less than 100 is a finite set.
Hence, the correct answer is option 'A' - 1 only.
An irrational number is a number that cannot be expressed as a fraction of two integers. It is a decimal that goes on forever without repeating.
To determine whether the set of all irrational numbers between 2 and 5 is infinite, we need to consider the nature of irrational numbers.
- There are infinitely many irrational numbers between any two rational numbers.
- The set of irrational numbers is not countable, meaning it cannot be listed in a finite or countable sequence.
Since the set of irrational numbers between 2 and 5 is a subset of the set of all irrational numbers, it follows that the set of irrational numbers between 2 and 5 is also infinite.
Therefore, statement 1 is correct.
Statement 2: The set of all odd integers less than 100 is a finite set.
To determine whether the set of all odd integers less than 100 is finite, we need to consider the definition of a finite set.
A finite set is a set that has a specific number of elements and can be counted or listed.
In this case, the set of all odd integers less than 100 includes numbers like 1, 3, 5, 7, 9, ... up to 99.
Since we can list or count all the elements in this set, it is a finite set.
Therefore, statement 2 is incorrect.
Conclusion:
- Statement 1 is correct as the set of all irrational numbers between 2 and 5 is infinite.
- Statement 2 is incorrect as the set of all odd integers less than 100 is a finite set.
Hence, the correct answer is option 'A' - 1 only.
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Consider the following statements :1. The set of all irrational numbers between 2 and 5 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?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'A'. Can you explain this answer?
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