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

From the above statements we can find the elements of the set.

So,

A = {2, 3, 7}

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

C = {1, 4, 5, 6}

*Prime numbers are the numbers which can only be divided by 1 or the number itself.

*Factors are the number which are multiplied together to get a new number so the term prime factorization may be defined as the finding the prime numbers which are multiplied together to give the source word.

The elements of B are natural number and they lies between 6 and 12.

Here we have to verify A (B C) = (A B) C. It’s the associative union property of set theory.

L.H.S.

A (B C)

Here first we will split the entire operation and have to find elements of (B C) using the given data then we will find the union of set A and the set obtained from the union of B and C

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

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

Now

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

= {2, 3, 7, 6, 8, 9, 10, 11, 12, 1, 4, 5}

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}…………..(1)

R.H.S

(A B) C

Here first we have to find the value of (A B) from the given data then we will find the union between the set obtained from (B C)

And C

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

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

Now

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

= {2, 3, 7, 6, 8, 9, 10, 11, 12, 1, 4, 5}

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}…………..(2)

So from (1) & (2) it’s clear that L.H.S. = R.H.S which verifies that

A (B C) = (A B) C.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Learn to Make Your Own Acid Rain and pH Paper at Home!27 mins
Consistent and Inconsistent Equations33 mins
Verb & Tenses46 mins
Electronic Configuration and Valency47 mins
Solar and Lunar Eclipse47 mins
Globalisation and its Impact29 mins
Industries and its Importance37 mins
Champ Quiz | Electrical Power and Heating31 mins
Surface Area and Volume49 mins
Metaphor and Simile41 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses