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The set {2x|x is any positive rational number } is
- a)an infinite set,
- b)a null set,
- c)a finite set,
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The set {2x|x is any positive rational number } isa)an infinite set,b)...
- The set {2^x | x is any positive rational number} is an infinite set.
- Rational numbers include both whole numbers and fractions.
- As x varies over all positive rationals, 2^x takes infinitely many distinct values.
- Therefore, the set is infinite, corresponding to option A.
- Rational numbers include both whole numbers and fractions.
- As x varies over all positive rationals, 2^x takes infinitely many distinct values.
- Therefore, the set is infinite, corresponding to option A.
Most Upvoted Answer
The set {2x|x is any positive rational number } isa)an infinite set,b)...
Explanation:
To understand the given set, we need to know the meaning of positive rational numbers. Rational numbers are the numbers which can be expressed in the form of p/q, where p and q are integers and q is not equal to 0.
Positive rational numbers are the numbers which are greater than 0 and can be expressed in the form of p/q, where p and q are positive integers.
Now, the given set is {2x|x is any positive rational number}. This means that we need to take any positive rational number and multiply it by 2 to get an element of the set.
Let's take some examples to understand this set:
- If we take x = 1/2, then 2x = 1 and 1 is a positive rational number. So, 1 is an element of the set.
- If we take x = 3/4, then 2x = 3/2 and 3/2 is a positive rational number. So, 3/2 is an element of the set.
- If we take x = 2, then 2x = 4 and 4 is not a positive rational number. So, 4 is not an element of the set.
From the above examples, we can see that for any positive rational number x, 2x is also a positive rational number. This means that we can keep multiplying any positive rational number by 2 and we will get infinite positive rational numbers.
Hence, the given set {2x|x is any positive rational number} is an infinite set.
Therefore, the correct answer is option A) an infinite set.
To understand the given set, we need to know the meaning of positive rational numbers. Rational numbers are the numbers which can be expressed in the form of p/q, where p and q are integers and q is not equal to 0.
Positive rational numbers are the numbers which are greater than 0 and can be expressed in the form of p/q, where p and q are positive integers.
Now, the given set is {2x|x is any positive rational number}. This means that we need to take any positive rational number and multiply it by 2 to get an element of the set.
Let's take some examples to understand this set:
- If we take x = 1/2, then 2x = 1 and 1 is a positive rational number. So, 1 is an element of the set.
- If we take x = 3/4, then 2x = 3/2 and 3/2 is a positive rational number. So, 3/2 is an element of the set.
- If we take x = 2, then 2x = 4 and 4 is not a positive rational number. So, 4 is not an element of the set.
From the above examples, we can see that for any positive rational number x, 2x is also a positive rational number. This means that we can keep multiplying any positive rational number by 2 and we will get infinite positive rational numbers.
Hence, the given set {2x|x is any positive rational number} is an infinite set.
Therefore, the correct answer is option A) an infinite set.
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Community Answer
The set {2x|x is any positive rational number } isa)an infinite set,b)...
Because X belong to many positive infinte values. So ans is (A) an infinte set
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