Question

Write the roster form of (x: x is a factor of 42)​

Answer 1

Answer:

For A = {x|x is a prime factor of 42}, B ={x|5 < x ≤ 12, x ∈ N} and C = {1,4,5,6} verify A U (B U C) = (A U B) U C.

Union of two sets :

The union of the sets A and B is the set of all the element that belongs to either A or B or both. It is denoted by A U B(“A union B”).

Set builder form or rule method :

In this method the elements are described by a common property of the members.

We can represent a set of by stating a property which its elements satisfy. Thus,the set of natural numbers less than 10 is,

A = {x | x is a natural number,x <10}

Or

A = {x : x is a natural number and x <10}

•We can read this as “ A is the set of all elements x such that x is a natural number and x is less than 10.”

• ∈ - belongs to

SOLUTION:

A = {x|x is a prime factor of 42}

A = {2,3,7}

B ={x|5 < x ≤ 12, x ∈ N}

B = {6,7,8,9,10,11,12}

C = {1,4,5,6}

L.H.S -:

A U (B U C)

(B U C) = {6,7,8,9,10,11,12} U {1,4,5,6}

= {1,4,5,6,7,8,9,10,11,12}

A U (B U C) = {2,3,7} U {1,4,5,6,7,8,9,10,11,12}

A U (B U C) = {1,2,3,4,5,6,7,8,9,10,11,12}

R.H.S -:

(A U B) U C

(A U B) = {2,3,7} U {6,7,8,9,10,11,12}

= {2,3,6,7,8,9,10,11,12}

(A U B) U C = {2,3,6,7,8,9,10,11,12} U {1,4,5,6}

(A U B) U C = {1,2,3,5,6,7,8,9,10,11,12}

L.H S = R.H.S

HOPE THIS WILL HELP YOU….

Step-by-step explanation:

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Answer 2

Answer:

The roster form of  (x: x is a factor of 42)​ =A={1 , 2, 3, 6, 7, 14, 21, 42}

Step-by-step explanation:

• we must know the set-builder notation, descriptive notation and roster notation.
• The set builder notation is a notation in which the set is described by using the properties of the elements . For example : Consider the set B = {2, 4, 6, 8, 10}. Here B is a set of elements which are positive and even numbers less than 12. So , the property of the elements of the set is that they are positive even numbers less than 12. So , the set B is represented in set builder form as: B = {x : x is a set of even natural numbers, 0 < x < 12} .
• The descriptive notation is a notation in which the property of the elements of a set is described using statements. For example: A = The set of all letters in the word MATHEMATICS.
• The roster notation is a notation in which all the elements of a set are listed between a pair of curly brackets { } and the elements are separated by commas. For example: B = {2, 4, 6, 8, 10}

Factors of 42 are simply numbers, more than two, which upon multiplication lead to the result or product of 42. Other important concepts for solving for factors are prime numbers, multiplication tables up to 20, negative and positive numbers.

• Let's discover the factors of 42 through the division method.
• Starting from the smallest number, let's find the common factors 42 by division method:
• Following the multiplication tables up to 20, we can easily find the factors of 42.
• The factors of 42 obtained are 42, 21, 14, 7, and 6.
• In order to know more factors of 42, we can start dividing 42 with the factors that we have obtained until now.
• With the above method, we have found 3 more new factors of 42 that are 1, 2, and 3. The common factors for 42 are 6 and 7.
• Therefore the total number of factors that 42 has is 8 and they are 1, 2, 3, 6, 7, 14, 21, and 42.
• A={1 , 2, 3, 6, 7, 14, 21, 42}