Question

*What will be the union set of Natural number set and Rational number set?*

1️⃣ Natural Number Set
2️⃣ Whole Number Set
3️⃣ Rational Number Set
4️⃣ Real Number Set​

Answer 1

The union set of Natural number set and Rational number set is called Rational Number Set.

• Natural numbers are defined as the counting numbers. It includes all the positive numbers from 1 to infinity.
• Note that zero is not included in natural numbers. All natural numbers along with zero are called whole numbers.
• Rational numbers are the ones which can be represented in the form of p/q. The rational number set is thus a broader category which encompasses natural numbers, whole numbers and integers.

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The union set of Natural number set and Rational number set

1. Natural Number Set

2. Whole Number Set

3. Rational Number Set

4. Real Number Set

CONCEPT TO BE IMPLEMENTED

SET

A set is a well defined collection of distinct objects of our perception or of our thought, to be conceived as a whole

Commonly we shall use capital letters A, B, C.... to denote sets and small letters a, b, c.... to denote objects ( or elements) of a set

UNION OF SETS

Let S and T are two sets. Then their union is denoted by S ∪ T and defined as

$\sf{S \cup T = \{ \:x : x \in \: S \: \:or \: \: x \in \: T \: \}}$

EVALUATION

Here two given sets are Natural number set and Rational number set

$\sf{Natural \: Number \: set \: is \: denoted \: by \: \mathbb{N}}$

$\sf{ \mathbb{N} = \{ \: 1,2,3,4,5........\: \}}$

$\sf{Rational \: Number \: set \: is \: denoted \: by \: \: \mathbb{ Q}}$

It is the set of all numbers of the form p/q where p and q are integers with q ≠ 0

$\sf{Suppose \: \: \: S = \mathbb{N} \cup \mathbb{Q}}$

CHECKING FOR OPTION : 1

$\sf{If \: \: \: S = \mathbb{N} }$

$\displaystyle \sf{ Then \: \: \frac{1}{2} \in \:\mathbb{Q} \: \: but \: \: \frac{1}{2} \notin \: S }$

So option 1 is not correct

CHECKING FOR OPTION : 2

If S = Whole number set

$\displaystyle \sf{ Then \: \: \frac{1}{2} \in \:\mathbb{Q} \: \: but \: \: \frac{1}{2} \notin \: S }$

So option 2 is not correct

CHECKING FOR OPTION : 3

Here every element of S is either an natural number or rational number

Also

$\sf{\mathbb{N} \subset \mathbb{Q}}$

$\sf{ \therefore \: \: \: \mathbb{N} \cup \mathbb{Q} =\mathbb{Q} }$

So this option is correct

CHECKING FOR OPTION : 4

If S = Real number Set

Then √3 ∈ S but √3 is neither a Natural number nor a Rational number

So this option is not correct

FINAL ANSWER

The union set of Natural number set and Rational number set

3. Rational Number Set

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