Question

*A = {x | x ∈ R, but x ∉ Q} Identify the type of set A.*

1️⃣ Set of natural numbers
2️⃣ Set of whole numbers
3️⃣ Set of integers
4️⃣ Set of irrational numbers​

Answer 1

Given :  A = {x | x ∈ R, but x ∉ Q}

To Find : Identify the type of set A.

1️⃣ Set of natural numbers

2️⃣ Set of whole numbers

3️⃣ Set of integers

4️⃣ Set of irrational numbers​

Solution:

Rational numbers are real numbers which can be written in the form p/q where p and q are integers and q≠0

All real numbers which are not rational  are irrationals.

A = {x | x ∈ R, but x ∉ Q}

R represents real Numbers

Q  represents Rational Numbers

as x is real number but rational hence x must be irrational

so

type of set A is Set of irrational numbers​

Natural numbers , whole numbers and  integers are subsets of Rational numbers   as x  ∉ Q ( rational number ) so  x does not belong to any of the set of natural numbers , integers and Whole number

Correct option is  4️⃣ Set of irrational numbers​

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

A = {x | x ∈ R, but x ∉ Q} Identify the type of set A

1. Set of natural numbers

2. Set of whole numbers

3. Set of integers

4. Set of irrational numbers

EVALUATION

Here the given set is

A = {x | x ∈ R, but x ∉ Q}

R is the set of real numbers and Q is the set of rational numbers

We know that set of real numbers R can be rewritten as the union ( more precisely direct sum) of two sets :

• Set of rational numbers Q

• Set of irrational numbers Q'

R = Q ∪ Q'

Now we have

A = {x | x ∈ R, but x ∉ Q}

= R - Q

= Q'

= Set of irrational numbers

FINAL ANSWER

Hence the correct option is

4. Set of irrational numbers

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