Sets

To solve this problem, we need to find the union of two sets: $(A%20%5Ccap%20B)$ and $(B%20%5Ccap%20C)$ .

Intersection of Set A and Set B:

Set $A%20%3D%20%5C%7B2%2C%204%2C%206%2C%208%2C%2010%2C%2012%5C%7D$ and Set $B%20%3D%20%5C%7B8%2C%2010%2C%2012%2C%2014%2C%2016%2C%2018%5C%7D$ .

The intersection $A%20%5Ccap%20B$ includes all elements common to both sets A and B.

$A%20%5Ccap%20B%20%3D%20%5C%7B8%2C%2010%2C%2012%5C%7D$ .

Intersection of Set B and Set C:

Set $B%20%3D%20%5C%7B8%2C%2010%2C%2012%2C%2014%2C%2016%2C%2018%5C%7D$ and Set $C%20%3D%20%5C%7B7%2C%208%2C%209%2C%2010%2C%2011%2C%2012%2C%2013%5C%7D$ .

The intersection $B%20%5Ccap%20C$ includes all elements common to both sets B and C.

$B%20%5Ccap%20C%20%3D%20%5C%7B8%2C%2010%2C%2012%5C%7D$ .

Union of Intersections:

The union of $A%20%5Ccap%20B$ and $B%20%5Ccap%20C$ combines all elements from both intersections, without repeating any elements.

$(A%20%5Ccap%20B)%20%5Ccup%20(B%20%5Ccap%20C)%20%3D%20%5C%7B8%2C%2010%2C%2012%5C%7D%20%5Ccup%20%5C%7B8%2C%2010%2C%2012%5C%7D%20%3D%20%5C%7B8%2C%2010%2C%2012%5C%7D$ .

Since both intersections are identical, the union remains the same set of elements.

Conclusion: The result of the operation $(A%20%5Ccap%20B)%20%5Ccup%20(B%20%5Ccap%20C)$ is the set $%5C%7B8%2C%2010%2C%2012%5C%7D$ . Therefore, the correct option is

{8, 10, 12}

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Sets

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs